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Protein Geometry, Function and Mutation

Robert PENNER

This survey for mathematicians summarizes several works by the author on protein geometry and protein function with applications to viral glycoproteins in general and the spike glycoprotein of the SARS-CoV-2 virus in particular. Background biology and bio

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Angle Defect for Super Triangles

Robert PENNER

We prove that the angle defect minus the area of a super hyperbolic triangle is not identically zero and explicitly compute the purely fermionic difference. This disproves the Angle Defect Theorem for N=1 super hyperbolic geometry and provides a no

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On quantum states over time

James FULLWOOD, Arthur PARZYGNAT

In 2017, D. Horsman, C. Heunen, M. Pusey, J. Barrett, and R. Spekkens proved that there is no physically reasonable assignment that takes a quantum channel and an initial state and produces a joint state on the tensor product of the input and output space

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Octonionic Clifford Algebra for the Internal Space of the Standard Model

Ivan TODOROV

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Bayesian inversion and the Tomita-Takesaki modular group

Luca GIORGETTI, Arthur PARZYGNAT, Alessio RANALLO, Benjamin RUSSO

We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita--Takesaki modular group and we

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On the origins of the Omicron variant of the SARS-CoV-2 virus

Robert PENNER, Minus VAN BAALEN

A possible explanation based on principles of speciation for the appearance of the Omicron variant of the SARS-CoV-2 virus is proposed involving coinfection with HIV. The gist of this is that the resultant HIV-induced immunocompromise allows SARS-CoV-2 g

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Mutagenic distinction between the receptor-binding and fusion subunits of the SARS-CoV-2 spike glycoprotein

Robert PENNER

We observe that a residue R of the spike glycoprotein of SARS-CoV-2 which has mutated in one or more of the current Variants of Concern or Interest and under Monitoring rarely participates in a backbone hydrogen bond if R lies in the S1 subunit and usuall

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Music of moduli spaces

Robert PENNER

A musical instrument, the plastic hormonica, is defined here as a birthday present for Dennis Sullivan, who pioneered and helped popularize the hyperbolic geometry underlying its construction. This plastic hormonica is based upon the Farey tesselati

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Relative topos theory via stacks

Olivia CARAMELLO, Riccardo ZANFA

We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site (C, J) and that of C-indexed categories. This repre

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The information loss of a stochastic map

James FULLWOOD, Arthur PARZYGNAT

We provide a stochastic extension of the Baez--Fritz--Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that w

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Noncommutative Differential K-theory

Byungdo PARK, Arthur PARZYGNAT, Corbett REDDEN, Augusto STOFFEL

We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression forms as well as a differential refinement of the smooth Serre-Swan correspon

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Tropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction

Daniel C. DOUGLAS, Zhe SUN

For a finite-type surface S, we study a preferred basis for the commutative algebra of regular functions on the SL3(C)-character variety, introduced by Sikora-Westbury. These basis elements come from the trace functions associated to certain tri-valent gr

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Cohomological Descent for Faltings' $p$-adic Hodge Theory and Applications

Tongmu HE

Faltings' approach in $p$-adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the $p$-adic n and then, the establishment of a link between the latter and differential forms. These relations

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The over-topos at a model

Olivia CARAMELLO, Axel OSMOND

With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, which we call the antecedent topology. Then we show that the associated sheaf

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Super Hyperbolic Law of Cosines: same formula with different content

Robert PENNER

We derive the Laws of Cosines and Sines in the super hyperbolic plane using Minkowski supergeometry and find the identical formulae to the classical case, but remarkably involving different expressions for cosines and sines of angles which include substan

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Antiviral Resistance against Viral Mutation: Praxis and Policy for SARS CoV-2

Robert PENNER

New tools developed by Moderna, BioNTech/Pfizer and Oxford/Astrazeneca provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method i

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Conditional distributions for quantum systems

Arthur PARZYGNAT

Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps are obtained via a categorical Bayesian inversion procedure. Simple criteria

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Superselection of the weak hypercharge and the algebra of the Standard Model

Ivan TODOROV

Restricting the $\mathbb{Z}_2$-graded tensor product of Clifford algebras $C\ell_4\hat{$C\ell_4^1$. We emphasize the role of the exactly conserved weak hypercharge Y, promoted here to a superselection rule for both observables and gauge transformation

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Sketch of a Program for Universal Automorphic Functions to Capture Monstrous Moonshine

Igor FRENKEL, Robert PENNER

We review and reformulate old and prove new results about the triad $ {\rm PPSL}_2({\mathbb Z})\subseteq{\rm PPSL}_2({\mathbb R})\circlearrowright ppsl_2({\mathbb R}) $, which provides a universal generalization of the classical automorphic t

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On Kontsevich Generalizations of Tian-Todorov Theorem and Applications

Lucian IONESCU

Kontsevich recently generalized Tian-Todorov Theorem regarding the structure of the Kuranish space of deformations of a Kahler manifold with trivial canonical bundle. An alternative proof was given using a general result regarding the smoothness of

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A functorial characterization of von Neumann entropy

Arthur PARZYGNAT

We classify the von Neumann entropy as a certain concave functor from finite- dimensional non-commutative probability spaces and state-preserving ∗-homomorphisms to real numbers. This is made precise by first showing that the category of non-commutative

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Denseness conditions, morphisms and equivalences of toposes

Olivia CARAMELLO

We systematically investigate morphisms and equivalences of toposes from multiple points of view. We establish a dual adjunction between morphisms and comorphisms of sites, introduce the notion of weak morphism of toposes and characterize the functors whi

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A characterization of complex quasi-projective manifolds uniformized by unit balls

Ya DENG

In 1988 Simpson extended the Donaldson-Uhlenbeck-Yau theorem to the context of Higgs bundles, and as an application he proved a uniformization theorem which characterizes complex projective manifolds and quasi-projective curves whose universal coverings a

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A non-commutative Bayes' theorem

Arthur PARZYGNAT, Benjamin RUSSO

Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras. In other words, we prove an analogue of Bayes' theorem in

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Backbone free energy estimator applied to viral glycoproteins

Robert PENNER

Proteins, Backbone Hydrogen Bonds, Backbone Free Energy, Viral Glycoproteins, Antiviral Vaccine/Drug TargetsEarlier analysis of the Protein Data Bank derived the distribution of rotations from the plane of a protein hydrogen bond donor peptide group

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Superconnection in the spin factor approach to particle physics

Michel DUBOIS-VIOLETTE, Ivan TODOROV

The notion of superconnection devised by Quillen in 1985 and used in gauge-Higgs field theory in the 1990's is applied to the spin factors (finite-dimensional euclidean Jordan algebras) recently considered as representing the finite quantum geometry of

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Les suites spectrales de Hodge-Tate

Ahmed ABBES, Michel GROS

This book presents two important results in p-adic Hodge theory following the approach initiated by Faltings, namely (i) his main p-adic comparison theorem, and (ii) the Hodge-Tate spectral sequence. We establish for each of these results two versions, an

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The relative Hodge-Tate spectral sequence - an overview

Ahmed ABBES, Michel GROS

We give in this note an overview of a recent work leading to a generalization of the Hodge-Tate spectral sequence to morphisms. The latter takes place in Faltings topos, but its construction requires the introduction of a relative variant of this topo

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Graphon Models in Quantum Physics

Ali SHOJAEI-FARD

In this work we explain some new applications of Infinite Combinatorics to Quantum Physics. We investigate the use of the theory of graphons in non-perturbative Quantum Field Theory and Deformation Quantization which lead us to discover some new interrela

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Big Picard theorem and algebraic hyperbolicity for varieties admitting a variation of Hodge structures

Ya DENG

For a complex smooth log pair \((Y,D)\), if the quasi-projective manifold \(U=Y-D\) admits a complex polarized variation of Hodge structures with local unipotent monodromies around \(D\) or admits an integral polarized variation of Hodge structures

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Inverses, disintegrations, and Bayesian inversion in quantum Markov categories

Arthur PARZYGNAT

We analyze three successively more general notions of reversibility and statistical inference: ordinary inverses, disintegrations, and Bayesian inferences. We provide purely categorical definitions of these notions and show how each one is a strictly spec

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Universal cocycles and the graph complex action on homogeneous Poisson brackets by diffeomorphisms

Ricardo BURING, Arthemy KISELEV

The graph complex acts on the spaces of Poisson bi-vectors $P$ by infinitesimal symmetries. We prove that whenever a Poisson structure is homogeneous, i.e. $P = L_{\vec{V}}(P)$ w.r.t. the Lie derivative along some vector field $\vec{V}$, but not quadrat

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Big Picard theorem for moduli spaces of polarized manifolds

Ya DENG

Consider a smooth projective family of complex polarized manifolds with semi-ample canonical sheaf over a quasi-projective manifold $V$. When the associated moduli map $V\to P_h$ from the base to coarse moduli space is quasi-finite, we prove that

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Topological Recursion, Airy structures in the space of cycles

Bertrand EYNARD

Topological recursion associates to a spectral curve, a sequence of meromorphic differential forms. A tangent space to the "moduli space" of spectral curves (its space of deformations) is locally described by meromorphic 1-forms, and we use form-cycl

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Vanishing theorem for tame harmonic bundles via $L^2$-cohomology

Ya DENG, Feng HAO

Using $L^2$-methods, we prove a vanishing theorem for tame harmonic bundles over quasi-Ka and for parabolic Higgs bundles by Arapura, Li and the second named author. To prove our vanishing theorem, we construct a fine resolution of the Dolbeault comp

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Construction of the classical time crystal Lagrangians from Sisyphus dynamics and duality description with the Liénard type equation

Partha GUHA, Anindya GHOSE-CHOUDHURY

We explore the connection between the equations describing sisyphus dynamics and the generic Liénard type or Liénard II equation from the viewpoint of branched Hamil- tonians. The former provides the appropriate setting for classical time crystal

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Equivariant connective K-theory

Nikita KARPENKO, Alexander MERKURJEV

For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective K-theory mapping to the equivariant K-homology of Guillot and the equivariant algebraic K-theo

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Pre-Calabi-Yau algebras and $\xi\partial$-calculus on higher cyclic Hochschild cohomology

Natalia IYUDU, Maxim KONTSEVICH

We formulate the notion of pre-Calabi-Yau structure via the higher cyclic Hochschild complex and study its cohomology. A small quasi-isomorphic subcomplex in higher cyclic Hochschild complex gives rise to the graphical calculus of $\xi\partial$-monomial

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Three-body closed chain of interactive (an)harmonic oscillators and the algebra $sl(4)$

Alexander TURBINER, Willard MILLER JR, Adrian ESCOBAR-RUIZ

In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative {\it distances}, $|{\bf r}_i - {\bf r}_j |$, between particles. The two-body harmonic oscillator is two-parametric and can be reduc

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On volume subregion complexity in Vaidya spacetime

Roberto AUZZI, Giuseppe NARDELLI, Fidel Ivan SCHAPOSNIK MASSOLO, Gianni TALLARITA, Nicolo ZENONI

We study holographic subregion volume complexity for a line segment in the AdS3 Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual conformal fiel

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Action potential solitons and waves in axons

Gaspar CANO, Rui DILãO

We show that the action potential signals generated inside axons propagate as reaction-diffusion solitons or as reaction-diffusion waves, refuting the Hodgkin and Huxley (HH) hypothesis that action potentials propagate along axons with an elastic wav

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Super McShane Identity

Yi HUANG, Robert PENNER, Anton ZEITLIN

The McShane identity for the once-punctured super torus is derived following Bowditch's proof in the bosonic case using techniques in super Teichmueller theory developed by the two latter-named authors.

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An electrophysiology model for cells and tissues

Rui DILãO

We introduce a kinetic model to study the dynamics of ions in aggregates of cells and tissues. Different types of communication channels between adjacent cells and between cells and intracellular space are considered (ion channels, pumps and gap junctio

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McShane identities for Higher Teichmuller theory and the Goncharov-Shen potential

Yi HUANG, Zhe SUN

In [GS15], Goncharov and Shen introduce a family of mapping class group invariant regular functions on their A-moduli space to explicitly formulate a particular homological mirror symmetry conjecture. Using these regular functions, we obtain McShane ident

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Third Kind Elliptic Integrals and 1-Motives

Cristiana BERTOLIN

In [5] we have showed that the Generalized Grothendieck's Conjecture of Periods applied to 1-motives, whose underlying semi-abelian variety is a product of elliptic curves and of tori, is equivalent to a transcendental conjecture involving elliptic integ

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Large genus behavior of topological recursion

Bertrand EYNARD

We show that for a rather generic set of regular spectral curves, the {\it Topological--Recursion} invariants $F_g$ grow at most like $O((\beta g)! r^{-g}) $ with some $r>0$ and $\beta\leq 5$

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Standard conjectures in model theory, and categoricity of comparison isomorphisms. A model theory perspective.

Misha GAVRILOVICH

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On Phases Of Melonic Quantum Mechanics

Frank FERRARI, Fidel I. SCHAPOSNIK MASSOLO

We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large D limit, or as disordered models. Both models have a mass parameter m and the transition f

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The lure of conformal symmetry

Ivan TODOROV

The Clifford algebra ${\rm Cl} (4,1) \simeq {\mathbb C} [4]$, generated by the real (Majorana) $\gamma$-matrices and by a hermitian $\gamma_5$, gives room to the reductive Lie algebra $u(2,2)$ of the conformal group extended by the $u(1)$ helicity op

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Hyperbolic endomorphisms and overlap numbers

Eugen MIHAILESCU

Hyperbolic endomorphisms and overlap numbers for equilibrium measures are studied on lifts of invariant sets. We look into the structure of Rokhlin conditional measures with respect to various fiber partitions, and find relations between them. We also co

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Some aspects of topological Galois theory

Olivia CARAMELLO, Laurent LAFFORGUE

We establish a number of results on the subject of the first author's topos-theoretic generalization of Grothendieck's Galois formalism. In particular, we generalize in this context the existence theorem of algebraic closures, we give a concrete d

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Three Hopf algebras from number theory, physics and topology, and their common operadic, simplicial and categorical background

Imma IMMA GALVEZ-CARRILLO, Ralph M. KAUFMANN, Andy TONKS

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. The primary examples are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renorm

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On the Ramanujan conjecture for automorphic forms over function fields I. Geometry

Will SAWIN, Nicolas TEMPLIER

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Global bifurcations of limit cycles in the Leslie-Gover model with the Allee effect

Valery A. GAIKO, Jean-Marc GINOUX, Cornelis VUIK

In this paper, we complete the global qualitative analysis of the Leslie-Gover system with the Allee effect which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global

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Multi-parameter planar polynomial dynamical systems

Valery GAIKO, Cornelis VUIK

In this paper, we study multi-parameter planar dynamical systems and carry out the global bifurcation analysis of such systems. To control the global bifurcations of limit cycle in these systems, it is necessary to know the properties and combine the effe

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Pre-Calabi-Yau algebras as noncommutative Poisson structures

Natalia IYUDU, Maxim KONTSEVICH

We show how the double Poisson algebra introduced in \cite{VdB} appear as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation on $Ac part of this solu

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Introduction to Higher Cubical Operads. Second Part: The Functor of Fundamental Cubical Weak $\infty$-Groupoids for Spaces

Camell KACHOUR

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Some Aspects of Dynamical Topology: Dynamical Compactness and Slovak Spaces

Sergiy KOLYADA

The area of dynamical systems where one investigates dynamical properties that can be described in topological terms is "Topological Dynamics". Investigating the topological properties of spaces and maps that can be described in dynamical

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From Euler's play with infinite series to the anomalous magnetic moment

Ivan TODOROV

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Introduction to Higher Cubical Operads. First Part: The Cubical Operad of Cubical Weak $\infty$-Categories

Camel KACHOUR

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``Ars combinatoria'' chez Gian-Carlo Rota ou le triomphe du symbolisme

Pierre CARTIER

Gian-Carlos Rota est l'inventeur d'une nouvelle science : la combinatoire algébrique qui n'était jusque-là qu'un ensemble de questions disparates, dont la solution, parfois ingénieuse, ne laissait entrevoir la méthode. Il s'agit ici de décrire

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Generalized conformal Hamiltonian dynamics and the pattern formation equations

Partha GUHA, Anindya GHOSE-CHOUDHURY

We demonstrate the significance of the Jacobi last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in the activator-inhibitor (AI) systems.

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Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy

Kumar ABHINAV, Partha GUHA, Indranil MUKHERJEE

The hierarchy of equations belonging to two different but related integrable systems, the Nonlinear Schrödinger and its derivative variant, DNLS are subjected to two distinct deformation procedures, viz. quasi-integrable deformation (QID) that gene

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Noncommutative Catalan Numbers

Arkady BERENSTEIN, Vladimir RETAKH

The goal of this paper is to introduce and study non-commutative Catalan numbers C_n which belong to the free Laurent polynomial algebra in n generators. Our non-commutative numbers admit interesting (commutative and non-commutative) specializations, one

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Theory of Morphogenesis

Andrey MINARSKY, Nadya MOROZOVA, Robert PENNER, Christophe SOULé

A model of morphogenesis is proposed based upon seven explicit postulates. The mathematical import and biological significance of the postulates are explored and discussed.

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Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription

Chris KAVANAGH, Donato BINI, Thibault DAMOUR, Seth HOPPER, Adrian C. OTTEWILL, Barry WARDELL

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Properties of soliton surfaces associated with integrable $\mathbb{C}P^{N-1}$ sigma models

Sanjib DEY, Alfred Michel GRUNDLAND

We investigate certain properties of $\\mathfrak{su}(N)$-valued two-dimensional soliton surfaces associated with the integrable $\\mathbb{C}P^{N-1}$ sigma models constructed by the orthogonal rank-one Hermitian projectors, which are defined on the two

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q-deformed quadrature operator and optical tomogram

M. P. JAYAKRISHNAN, Sanjib DEY, Mir FAIZAL, C. SUDHEESH

In this paper, we define the homodyne q-deformed quadrature operator and find its eigenstates in terms of the deformed Fock states. We find the quadrature representation of q-deformed Fock states in the process. Furthermore, we calculate the explicit anal

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SKEW PRODUCT SMALE ENDOMORPHISMS OVER COUNTABLE SHIFTS OF FINITE TYPE

EUGEN MIHAILESCU, Mariusz URBANSKI

We introduce and study skew product Smale endomorphisms over finitely irreducible topological Markov shifts with countable alphabets. We prove that almost all conditional measures of equilibrium states of summable and locally Holder continuous potentia

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M-theoretic Lichnerowicz formula and supersymmetry

André COIMBRA, Ruben MINASIAN

A suitable generalisation of the Lichnerowicz formula can relate the squares of supersymmetric operators to the effective action, the Bianchi identities for fluxes, and some equations of motion. Recently, such formulae have also been shown to underl

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Modification of Schrodinger-Newton equation due to braneworld models with minimal length

Anha BHAT, Sanjib DEY, Mir FAIZAL, Chenguang HOU, Qin ZHAO

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation o

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Quantum Supersymmetric Cosmological Billiards and their Hidden Kac-Moody Structure

Thibault DAMOUR, Philippe SPINDEL

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Software modules and computer-assisted proof schemes in the Kontsevich deformation quantization

Ricardo BURING, Arthemy V. KISELEV

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these al

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Galois equivariance of critical values of $L$-functions for unitary groups

Lucio GUERBEROFF, Jie LIN

The goal of this paper is to provide a refinement of a formula proved by the first author which expresses some critical values of automorphic $L$-functions on unitary groups as Petersson norms of automorphic forms. Here we provide a Galois equivariant ver

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Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra

Ivan TODOROV, Michel DUBOIS-VIOLETTE

We continue the study undertaken in [DV] of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known properties of $J$ and of

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Examples of pre-CY structures, associated operads and cohomologies

Natalia IYUDU

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On the four-loop static contribution to the gravitational interaction potential of two point masses

Thibault DAMOUR, Piotr JARANOWSKI

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Three-body problem in 3D space: ground state, (quasi)-exact-solvability

Alexander V TURBINER, Willard MILLER JR, Adrian M ESCOBAR-RUIZ

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Diffeomorphisms of quantum fields

Dirk KREIMER, Karen YEATS

We study field diffeomorphisms $\Phi(x)= F(\rho(x))=a_0\rho(x)+a_1\rho^2(x)+\ldots=\sum_{j+0}^\infty a_j \rho^{j+1}, $ for free and interacting quantum fields $\Phi$. We find that the theory is invariant under such diffeomorphisms if and only

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Sur la dualité des topos et de leurs présentations et ses applications : une introduction

Olivia CARAMELLO, Laurent LAFFORGUE

Ce texte est une version écrite enrichie des notes d'un exposé donné à l'Université de Nantes le 1er avril 2016. Il a été rédigé par le second auteur, à partir de notes succinctes et d'expositions orales du premier auteur. Il peut servir d'i

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Le principe de fonctorialité de Langlands comme un problème de généralisation de la loi d'addition

Laurent LAFFORGUE

Ce texte représente les notes écrites d'un cours donné à l'Université de Nottingham en juin 2016. Dans la continuité des écrits précédents de l'auteur, il étudie le transfert automorphe de Langlands des groupes réductifs vers les grou

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Algebraic flows on Shimura varieties

Emmanuel ULLMO, Andrei YAFAEV

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Holomorphic curves in compact Shimura varieties

Emmanuel ULLMO, Andrei YAFAEV

We prove a hyperbolic analogue of the We prove an analogue of the Bloch-Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties.

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Structures spéciales et problème de Zilber-Pink

Emmanuel ULLMO

The Manin-Mumford and the André-Oort conjectures as well as the one formulated by Zilber and Pink concern algebraic varieties (algebraic tori, Abelian or semi-Abelian varieties, pure or mixed Shimura varieties) endowed with a natural set of special p

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Bi-algebraic geometry and the André-Oort conjecture

Bruno KLINGLER, Emmanuel ULLMO, Andrei YAFAEV

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O-minimal flows on abelian varieties

Emmanuel ULLMO, Andrei YAFAEV

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Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory

Thibault DAMOUR

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Golod-Shafarevich type theorems and potential algebras

Natalia IYUDU, Agata SMOKTUNOWICZ

Potential algebras feature in the minimal model program and noncommutative resolution of singularities, and the important cases are when they are finite dimensional, or of linear growth. We develop techniques, involving Groebner basis theory and gene

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Divisor Braids

Marcel BOKSTEDT, Nuno ROMAO

We study a novel type of braid groups on a closed orientable surface Σ. These are fundamental groups of certain manifolds that are hybrids between symmetric products and configuration spaces of points on Σ; a class of examples arises naturally in gauge

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One question from the Polishchuk and Positselski book on Quadratic algebras

Natalia IYUDU, Stanislav SHKARIN

In the book 'Quadratic algebras' due to Polishchuk and Positselski algebras with small number of generators (n=2,3) is considered. For some number of relations r possible Hilbert series are listed, and those appearing as series of Koszul algebras a

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On the proof of the homology conjecture for monomial non-unital algebras

Natalia IYUDU

We consider the bar complex of a monomial non-unital associative algebra A=k <X> / (w_1,...,w_t). For any fixed monomial w=x_1..x_n in A one can define certain subcomplex of the Bar complex of A. It was conjectured in [3] that homology of this complex is

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Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

Fei HU, Sheng-Li TAN, De-Qi ZHANG

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Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism

Donato BINI, Thibault DAMOUR

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Do the Kontsevich tetrahedral flows preserve or destroy the space of Poisson bi-vectors?

Anass BOUISAGHOUANE, Arthemy KISELEV

We examine two claims from the paper "Formality Conjecture" (Ascona 1996): specifically, that 1) a certain tetrahedral graph flow preserves the class of (real-analytic) Poisson structures, and that 2) another tetrahedral graph flow vanishes at every suc

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BADLY APPROXIMABLE VECTORS AND FRACTALS DEFINED BY CONFORMAL DYNAMICAL SYSTEMS

Tushar DAS, Lior FISHMAN, David SIMMONS, Mariusz URBANSKI

We prove that if J is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors form a set of full Hausdorff dimension in J. The same is true if J is t

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Real Analyticity for random dynamics of transcendental functions

Volker MAYER, Mariusz URBANSKI, Anna ZDUNIK

Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh \cite{Rug08} leading to a simple approach to analyticity. W

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SU(N) transitions in M-theory on Calabi-Yau fourfolds and background fluxes

Hans JOCKERS, Sheldon KATZ, David MORRISON, M. Ronen PLESSER

We study M-theory on a Calabi-Yau fourfold with a smooth surface S of AN−1 singularities. The resulting three-dimensional theory has a =2 SU(N) gauge theory sector, which we obtain from a twisted dimensional reduction of a seven-dimensional =1 SU(

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New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole

Donato BINI, Thibault DAMOUR, Andrea GERALICO

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High post-Newtonian order gravitational self-force analytical results for eccentric orbits around a Kerr black hole

Donato BINI, Thibault DAMOUR, Andrea GERALICO

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Intermittency in the Hodgkin-Huxley model

Gaspar CANO, Rui DILAO

We show that action potentials in the Hodgkin-Huxley neuron model result from a type I intermittency phenomenon that occurs in the proximity of a saddle-node bifurcation of limit cycles. For the Hodgkin-Huxley spatially extended model, describing propag

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The Langlands-Shahidi method over function fields: the Ramanujan Conjecture and the Riemann Hypothesis for the unitary groups

Luis LOMELI

On étudie la méthode de Langlands-Shahidi sur les corps de fonctions de caractéristique p. On prouve la fonctorialité de Langlands globale et locale des groupes unitaires vers les groupes linéaires pour les représentations génériques. Supposant co

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Class number problems and Lang conjectures

Ayberk ZEYTIN

Given a square-free integer d we introduce an affine hypersurface whose integer points are in one-to-one correspondence with ideal classes of the quadratic number field Q(\sqrt{d}). Using this we relate class number problems of Gauss to Lang conjectur

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On Emergent Geometry from Entanglement Entropy in Matrix Theory

Vatche SAHAKIAN

Using Matrix theory, we compute the entanglement entropy between a supergravity probe and modes on a spherical membrane. We demonstrate that a membrane stretched between the probe and the sphere entangles these modes and leads to an expression for the e

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On the conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity

Thibault DAMOUR, Piotr JARANOWSKI, Gerhard SCHAEFER

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Modular Graph Functions

Eric D'HOKER, Michael B. GREEN, Omer GURDOGAN, Pierre VANHOVE

We consider properties of modular graph functions, which are non-holomorphic modular functions associated with the Feynman graphs for a conformal scalar field theory on a two-dimensional torus. Such functions arise, for example, in the low energy expansio

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Cutkosky Rules and Outer Space

Spencer BLOCH, Dirk KREIMER

We derive Cutkosky’s theorem starting from Pham’s classical work. We emphasize structural relations to Outer Space.

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Higher Chern classes in Iwasawa theory

F.M. BLEHER, T. CHINBURG, R. GREENBERG, M. KAKDE, G. PAPPAS, R. SHARIFI, M.J. TAYLOR

We begin a study of m-th Chern classes and m-th characteristic symbols for Iwasawa modules which are supported in codimension at least m. This extends the classical theory of characteristic ideals and their generators for Iwasawa modules which are torsion

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Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole

Donato BINI, Thibault DAMOUR, Andrea GERALICO

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Minisuperspace quantum supersymmetric cosmology (and its hidden hyperbolic Kac-Moody structures)

Thibault DAMOUR, Philippe SPINDEL

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Persistent homology and string vacua

Michele CIRAFICI

We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homolo

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Catégories syntactiques pour les motifs de Nori

Laurent LAFFORGUE

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A new effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

Simone BALMELLI, Thibault DAMOUR

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Spin-dependent two-body interactions from gravitational self-force computations

Donato BINI, Thibault DAMOUR, Andrea GERALICO

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BPS spectra, barcodes and walls

Michele CIRAFICI

BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper we approach th

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Moduli Spaces and Macromolecules

R. C. PENNER

Techniques from moduli spaces are applied to biological macromolecules. The first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally. The second main result identifies up to homotopy the

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Smoothness and classicality on eigenvarieties

Christophe BREUIL, Eugen HELLMANN, Benjamin SCHRAEN

Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of "classical weight" and that its Galois representation is crystalline at places dividing p, then f is conjectured

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A program for branching problems in the representation theory of real reductive groups

Toshiyuki KOBAYASHI

We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and analytic approache

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Decorated super-Teichmueller space

R. C. PENNER, Anton M. ZEITLIN

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La suite spectrale de Hodge-Tate

Ahmed ABBES, Michel GROS

The Hodge-Tate spectral sequence for a proper smooth variety over a p-adic field provides a framework for us to revisit Faltings' approach to p-adic Hodge theory and to fill in many details. The spectral sequence is obtained from the Cartan-Leray spectr

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On the modular structure of the genus-one Type II superstring low energy expansion

Eric D'HOKER, Michael B. GREEN, Pierre VANHOVE

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the

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Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus

Eric D'HOKER, Michael B. GREEN, Pierre VANHOVE

The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a torus. In the case of

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More Graviton Physics

Niels BJERRUM-BOHR, Barry HOLSTEIN, Ludovic PLANTé, Pierre VANHOVE

The interactions of gravitons with spin-1 matter are calculated in parallel with the well known photon case. It is shown that graviton scattering amplitudes can be factorized into a product of familiar electromagnetic forms, and cross sections f

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Fractal Tube Formulas and a Minkowski Measurability Criterion for Compact Subsets of Euclidean Spaces

Michel L. LAPIDUS, Goran RADUNOVIC, Darko ZUBRINIC

We establish fractal tube formulas valid for a large class of compact subsets (and more generally, relative fractal drums, RFDs) in Euclidean spaces of any dimension. These formulas express the volume of the tubular neighborhoods of the fractal under cons

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Fractal Zeta Functions and Complex Dimensions of Relative Fractal Drums

Michel L. LAPIDUS, Goran RADUNOVIC, Darko ZUBRINIC

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Distance and Tube Zeta Functions of Fractals and Arbitrary Compact Sets

Michel L. LAPIDUS, Goran RADUNOVIC, Darko ZUBRINIC

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Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory

Michel L. LAPIDUS, Goran RADUNOVIC, Darko ZUBRINIC

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Deformation approach to quantisation of field models

Arthemy V. KISELEV

Associativity-preserving deformation quantisation via Kontsevich's summation over weighted graphs is lifted from the algebras of functions on finite-dimensional Poisson manifolds to the algebras of local functionals within the variational Poisson geometr

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The Sound of Fractal Strings and the Riemann Hypothesis

Michel L. LAPIDUS

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Towards Quantized Number Theory: Spectral Operators and an Asymmetric Criterion for the Riemann Hypothesis

Michel L. LAPIDUS

An asymmetric criterion for the Riemann hypothesis is provided, expressed in terms of the invertibility of the spectral operator. This criterion is asymmetric, in the sense that it is valid for all fractal dimensions c in (0,1/2) if and only if the Rieman

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Energetics and phasing of nonprecessing spinning coalescing black hole binaries

Alessandro NAGAR, Thibault DAMOUR, Christian REISSWIG, Denis POLLNEY

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Deformations of complex structures on Riemann surfaces and integrable structures of Whitham type hierarchies

Alexander ODESSKII

We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space which corr

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On the large-scale geometry of the $L^p$-metric on the symplectomorphism group of the two-sphere

Michael BRANDENBURSKY, Egor SHELUKHIN

We prove that the vector space $R^d$ of any finite dimension $d$ with the standard metric embeds in a bi-Lipschitz way into the group of area-preserving diffeomorphisms of the two-sphere endowed with the $L^p$-metric for $p>2$. Along the way we show that

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The Equivalence Principle in a Quantum World

N. Emil J. BJERRUM-BOHR, John DONOGHUE, Basem EL-MENOUFI, Barry HOLSTEIN, Ludovic PLANT, Pierre VANHOVE

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Lectures on Regular and Irregular Holonomic D-modules

Masaki KASHIWARA, Pierre SCHAPIRA

This is a survey paper based on lectures given by the authors at Ihes, February/March 2015. In a first part, we recall the main results on the tempered holomorphic solutions of D-modules in the language of indsheaves and, as an application, the Riem

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Fourth post-Newtonian effective one-body dynamics

Thibault DAMOUR, Piotr JARANOWSKI, Gerhard SCHAEFER

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Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession

Donato BINI, Thibault DAMOUR

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Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions

Donato BINI, Thibault DAMOUR

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Differential symmetry breaking operators I. General theory and F-method

Toshiyuki KOBAYASHI, Michael PEVZNER

We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of t

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Differential symmetry breaking operators. II. Rankin--Cohen operators for symmetric pairs

Toshiyuki KOBAYASHI, Michael PEVZNER

Rankin--Cohen brackets are symmetry breaking operators for the tensor product of two holomorphic discrete series representations of SL(2,R). We address a general problem to find explicit formulae, for such intertwining operators in the setting of multipl

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Global uniqueness of small representations

Toshiyuki KOBAYASHI, Gordan SAVIN

We prove that automorphic representations whose local components are certain small representations have multiplicity one. The proof is based on the multiplicity-one theorem for certain functionals of small representations, also proved in this paper.

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On the integral law of thermal radiation

Yuri GUSEV

The integral law of thermal radiation by finite size emitters is studied. Two geometrical characteristics of a radiating body or a cavity, its volume and its boundary area, define two terms in its radiance. The term defined by the volume corresponds to t

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On weight modules of algebras of twisted differential operators on the projective space

Dimitar GRANTCHAROV, Vera SERGANOVA

We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on P^n. Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul are provided. We

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Topological invariants in magnetohydrodynamics and DNA supercoiling

Michael MONASTYRSKY, Pavel SASOROV

We discuss the structure of topological invariants in two different media. The first example relates to the problem of reconnection in magnetohydrodynamics and the second one to the supercoiling of DNA. Despite the apparently different systems

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$r_\infty$-Matrices, triangular $L_\infty$-bialgebras, and quantum$_\infty$ groups

Denis BASHKIROV, Alexander A. VORONOV

A homotopy analogue of the notion of a triangular Lie bialgebra is proposed with a goal of extending the basic notions of theory of quantum groups to the context of homotopy algebras and, in particular, introducing a homotopical generalization of the noti

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The calculus of multivectors on noncommutative jet spaces

Arthemy V. KISELEV

The Leibniz rule for derivations is invariant under cyclic permutations of the co-multiples within the derivations' arguments. We now explore the implications of this fundamental principle, developing the calculus of variations on the infinite jet spaces

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Smooth approximation of plurisubharmonic functions on almost complex manifolds

F. Reese HARVEY, H. Blaine LAWSON, JR., Szymon PLI\'S

This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic exhaustion fun

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Une interprétation modulaire de la variété trianguline

Christophe BREUIL, Eugen HELLMANN, Benjamin SCHRAEN

En utilisant le système de Taylor-Wiles-Kisin construit dans un travail récent de Caraiani, Emerton, Gee, Geraghty, Paškūnas et Shin, nous construisons un analogue de la variété de Hecke. Nous montrons que cette variété coïncide avec une union de

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The BV formalism for L$_\infty$-algebras

Denis BASHKIROV, Alexander A. VORONOV

The notions of a BV$_\infty$-morphism and a category of BV$_\infty$-algebras are investigated. The category of L$_\infty$-algebras with L$_\infty$-morphisms is characterized as a certain subcategory of the category of BV$_\infty$-algebras. T

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Graviton-Photon Scattering

N. E. J. BJERRUM-BOHR, B. R. HOLSTEIN, L. PLANT\'E, P. VANHOVE

We use that the gravitational Compton scattering factorizes on the Abelian QED amplitudes to evaluate various gravitational Comp- ton processes. We examine both the QED and gravitational Compton scattering from a massive spin-1 system by the use of helici

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Three dimensional Sklyanin algebras and Groebner bases

Natalia IYUDU, Stanislav SHKARIN

We consider a Sklyanin algebra S with 3 generators, which is the quadratic algebra over a field K with 3 generators x,y,z given by 3 relations pxy+qyx+rzz=0, pyz+qzy+rxx=0 and pzx+qxz+ryy=0. This class of algebras enjoyed much of attention, in particular,

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On Koszulity for operads of Conformal Field Theory

Natalia IYUDU, Abdenacer MAKHLOUF

We study two closely related operads: the Gelfand-Dorfman operad GD and the Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal algebra structure. We prove Koszulity of the Conformal Lie operad using the Gr ̈bner bases theory

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The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations

Natalia IYUDU, Stanislav SHKARIN

For an arbitrary associative unital ring R, let J1 and J2 be the following noncommutative birational partly defined involutions on the set M3 (R) of 3 × 3 matrices over R: J1 (M ) = M −1 (the usual matrix inverse) and J2 (M )jk = (Mkj )−1 (the transp

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Topos-theoretic background

Olivia CARAMELLO

This text, which will form the first chapter of my book in preparation "Lattices of theories", is a self-contained introduction to topos theory, geometric logic and the 'bridge' technique.

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Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective

Olivia CARAMELLO, Anna Carla RUSSO

We establish, generalizing Di Nola-Lettieri's categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not bi-interpretable in t

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Quasi-exact-solvability of the $A_2$ elliptic model: Algebraic form, $sl(3)$ hidden algebra, polynomial eigenfunctions

Vladimir V. SOKOLOV, Alexander V. TURBINER

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Dimensional exactness of self-measures for random countable iterated function systems with overlaps.

Eugen MIHAILESCU, Mariusz URBANSKI

We study projection measures for random countable (finite or infinite) conformal iterated function systems with arbitrary overlaps. In this setting we extend Feng's and Hu's result from [6] about deterministic finite alphabet iterated function system

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Principe de fonctorialité et transformations de Fourier non linéaires : proposition de définitions et esquisse d'une possible (?) démonstration

Laurent LAFFORGUE

Ce texte rassemble les notes écrites d'une série de quatre exposés donnés à l'IHES les 19 juin, 26 juin, 3 juillet et 8 juillet 2014. Il introduit une nouvelle approche pour une éventuelle démonstration - encore à vérifier - du transfert

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Extensions of flat functors and theories of presheaf type

Olivia CARAMELLO

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a characterization theore

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Cyclic theories

Olivia CARAMELLO, Nicholas WENTZLAFF

We describe a geometric theory classified by Connes-Consani's epicylic topos and two related theories respectively classified by the cyclic topos and by the topos $[{\mathbb N}^{\ast}, \Set]$.

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A Feynman integral via higher normal functions

Spencer BLOCH, Matt KERR, Pierre VANHOVE

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given

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Beltrami-Courant Differentials and $G_{\infty}$-algebras

Anton ZEITLIN

Using the symmetry properties of two-dimensional sigma models, we introduce a notion of the Beltrami-Courant differential, so that there is a natural homotopy Gerstenhaber algebra related to it. We conjecture that the generalized Maurer-Cartan equati

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2-CY-tilted algebras that are not Jacobian

Sefi LADKANI

Over any field of positive characteristic we construct 2-CY-tilted algebras that are not Jacobian algebras of quivers with potentials. As a remedy, we propose an extension of the notion of a potential, called hyperpotential, that allows to prove that cert

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Algebras of quasi-quaternion type

Sefi LADKANI

We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe that symmetric ta

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SL(2,Z)-invariance and D-instanton contributions to the $D^6 R^4$ interaction

Michael B. GREEN, Stephen D. MILLER, Pierre VANHOVE

The modular invariant coefficient of the $D^6R^4$ interaction in the low energy expansion of type~IIB string theory has been conjectured to be a solution of an inhomogeneous Laplace eigenvalue equation, obtained by considering the toroidal compactif

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Algebraic rational cells, equivariant intersection theory, and Poincaré duality

Richard Paul GONZALES VILCARROMERO

We provide a notion of algebraic rational cell with applications to intersection theory on singular varieties with torus action. Based on this notion, we study the algebraic analogue of Q-fi ltrable varieties: algebraic varieties where a torus acts with i

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Motivic Cohomology Spectral Sequence and Steenrod Algebra

Serge YAGUNOV

For an odd prime number $p$, it is shown that differentials $d_n$ in the motivic cohomology spectral sequence with $p$-local coefficients vanish unless $p-1$ divides $n-1$. We obtain an explicit formula for the first non-trivial differential $d_p$, ex

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Boundedness of non-homogeneous square functions and $L^q$ type testing conditions with $q \in (1,2)$

Henri MARTIKAINEN, Mihalis MOURGOGLOU

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Calculabilité de la cohomologie étale modulo l

David A. MADORE, Fabrice ORGOGOZO

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Scattering Equations and String Theory Amplitudes

Emil BJERRUM-BOHR, Poul DAMGAARD, Piotr TOURKINE, Pierre VANHOVE

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit, and

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Localization in equivariant operational K-theory and the Chang-Skjelbred property

Richard Paul GONZALES VILCARROMERO

We establish a localization theorem of Borel-Atiyah-Segal type for the equivariant operational K-theory of Anderson and Payne. Inspired by the work of Chang-Skjelbred and Goresky-Kottwitz-MacPherson, we establish a general form of GKM theory in this setti

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The physics of quantum gravity

Pierre VANHOVE

Quantum gravity is still very mysterious and far from being well under- stood. In this text we review the motivations for the quantification of gravity, and some expected physical consequences. We discuss the remarkable rela- tions between scattering proc

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Polylogarithms and multizeta values in massless Feynman amplitudes

Ivan TODOROV

The last two decades have seen a remarkable development of analytic methods in the study of Feynman amplitudes in perturbative quantum field theory. The present lecture offers a physicists' oriented survey of Francis Brown's work on singlevalued multipl

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Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability

Willard MILLER JR, Alexander V TURBINER

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The physics and the mixed Hodge structure of Feynman integrals

Pierre VANHOVE

This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining that

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Du transfert automorphe de Langlands aux formules de Poisson non linéaires

Laurent LAFFORGUE

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Non-Abelian Lie algebroids over jet spaces

Arthemy V. KISELEV, Andrey O. KRUTOV

We associate Hamiltonian homological evolutionary vector fields -- which are the non-Abelian variational Lie algebroids' differentials -- with Lie algebra-valued zero-curvature representations for partial differential equations.

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Une loi de réciprocité explicite pour le polylogarithme elliptique

Francesco LEMMA, Shanwen WANG

On démontre une compatibilité entre la réalisation p-adique et la réalisation de de Rham des sections de torsion du profaisceau polylogarithme elliptique. La preuve utilise une variante pour H1 de la loi de réciprocité explicite de Kato pour le H2 d

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Le système d'Euler de Kato (II)

Shanwen WANG

Ce texte est le deuxième article d’une série de trois articles sur une généralisation de système d’Euler de Kato. Il est consacré e d’Euler de Kato raffiné associé systèmes d’Euler de Kato.

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Topological pressure and measure-theoretic degrees for non-expanding transformations

Eugen MIHAILESCU, Mariusz URBANSKI

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Density of potentially crystalline representations of fixed weight

Eugen HELLMANN, Benjamin SCHRAEN

Let K be a finite extension of Qp. We fix a continuous absolutely irreducible representation of the absolute Galois group of K over a finite dimensional vector space with coefficient in a finite field of characteristic p and consider its universal deforma

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Eigenvalues of Laplacian and multi-way isoperimetric constants on weighted Riemannian manifolds

Kei FUNANO

We investigate the distribution of eigenvalues of the weighted Laplacian on closed weighted Riemannian manifolds of nonnegative Bakry-s. These inequalities are quantitative versions of the previous theorem by the author with Shioya. We also study some geo

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Ergostructures, Ergologic and the Universal Learning Problem: Chapters 1, 2, 3

Misha GROMOV

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The elliptic dilogarithm for the sunset graph

Spencer BLOCH, Pierre VANHOVE

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The geometry of variations in Batalin-Vilkovisky formalism

Arthemy KISELEV

We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "delta(0)=0" and "log delta(0)=0" within BV-approach to quantisation of gauge systems

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On-shell Techniques and Universal Results in Quantum Gravity

N.E.J. BJERRUM-BOHR, John F. DONOGHUE, Pierre VANHOVE

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Quantum supersymmetric cosmology and its hidden Kac--Moody structure

Thibault DAMOUR, Philippe SPINDEL

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Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation

Donato BINI, Thibault DAMOUR

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Merger states and final states of black hole coalescences: a numerical-relativity-assisted effective-one-body approach

Thibault DAMOUR, Alessandro NAGAR, Loic VILLAIN

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The tensor hierarchy simplified

Jesper GREITZ, Paul HOWE, Jakob PALMKVIST

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The Nielsen and the Reidemeister Zeta Functions of maps on infra-solvmanifolds of type (R)

Alexander FELSHTYN, Jong Bum LEE

We prove the rationality, the functional equations and calculate the radii of convergence of the Nielsen and the Reidemeister zeta functions of continuous maps on infra-solvmanifolds of type (R). We find a connection between the Reidemeister and Nielse

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Anyon wave functions and probability distributions

Douglas LUNDHOLM

The problem of determining the ground state energy for a quantum gas of anyons in two dimensions is considered. A recent approach to this problem by means of lower bounds is here refined to bring out the dependence on the n-particle probability distributi

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Ramification and nearby cycles for l-adic sheaves on relative curves

Haoyu HU

Deligne and Kato proved a formula computing the dimension of the nearby cycles complex of an l-adic sheaf on a relative curve over an excellent strictly henselian trait. In this article, we reprove this formula using Abbes-Saito’s ramification the

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Conformal and Einstein gravity in twistor space

Tim ADAMO, Lionel MASON

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Distributional Geometry of Squashed Cones

Dmitri FURSAEV, Alexander PATRUSHEV, Sergey SOLODUKHIN

A regularization procedure developed in \cite{Fursaev:1995ef} for integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have r

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Nonholonomic deformation of coupled and supersymmetric KdV equation and Euler-Poincaré-Suslov method

Partha GUHA

Recently Kupershmidt \cite{Kup} presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al \cite{KKK}. In this paper we demonstrate that Kupershmidt's method can be interpreted as an infin

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Application of Jacobi's last multiplier for construction of singular Hamiltonian of the activator-inhibitor model and conformal Hamiltonian dynamics

Partha GUHA, Anindya GHOSE CHOUDHURY

The relationship between Jacobi's last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by expli

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The role of the Jacobi Last Multiplier in Nonholonomic Systems and Almost Symplectic Structure

Partha GUHA

The relationship between Jacobi's last multiplier (JLM) and nonholonomic systems endowed with the almost symplectic structure is elucidated in this paper. In particular, we present an algorithmic way to describe how the two form and almost Poisson

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Contiguity relations for linearisable systems of Gambier type

Alfred RAMANI, Basil GRAMMATICOS, Partha GUHA

We introduce the Schlesinger transformations for the Gambier, linearisable, equation and by combining the former construct the contiguity relations of the solutions of the latter. We extend the approach to the discrete domain obtaining thus the Schlesinge

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Quantum aspects of the Liénard II equation and Jacobi's Last Multiplier-II

Anindya GHOSE CHOUDHURY, Partha GUHA

This is a continuation of the paper [J. Phys. A: Math. Theor. 46 (2013) 165202], in which we mapped the Lis ordering technique. In this paper we present further results on the construction of three sets of exactly solvable potentials giving rise

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Chemotherapy in heterogeneous cultures of cancer cells with interconversion

Rui DILãO

Recently, it has been observed the interconversion between differentiated and stem-like cancer cells. Here, we model the \textit{in vitro} growth of heterogeneous cell cultures in the presence of interconversion from differentiated cancer cells to

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Nouveaux développements sur les valeurs des caractères des groupes symétriques; méthodes combinatoires

Pierre CARTIER

L’étude asymptotique des diagrammes de Young de grande taille a été entreprise cu dans le but de contrôler les algèbres d’opérateurs liées aux groupes libres ; elles ont servi ensuite tude des zéros de la fonction zeta de Riemann. Plus réc

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Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function

Hafedh HERICHI, Michel L. LAPIDUS

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mRNA diffusion as a mechanism of morphogenesis in Drosophila early development

Rui DILãO

In Drosophila early development, bicoid mRNA of maternal origin is deposited in one of the poles of the egg, determining the anterior tip of the embryo and the position of the head of larvae. The deposition of mRNAs is done during oogenesis by the mother

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Equivariant operational Chow rings of spherical varieties and T-linear varieties.

Richard Paul GONZALES VILCARROMERO

We stablish localization theorems for the equivariant operational Chow rings (or equivariant Chow cohomology) of singular spherical varieties and T-linear varieties. Our main results provide a GKM description of these rings in the case of spherical var

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Dynamic trajectory control of gliders

Rui DILãO, João FONSECA

A new dynamic control algorithm in order to direct the trajectory of a glider to a pre-assigned target point is proposed. The algorithm runs iteratively and the approach to the target point is self-correcting. The algorithm is applicable to any non-p

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Chemotaxis with directional sensing during Dictyostelium aggregation

Rui DILãO, Marcus HAUSER

With an in silico analysis, we show that the chemotactic movements of colonies of the starving amoeba Dictyostelium discoideum are driven by a force that depends on both the direction of propagation (directional sensing) of reaction-diffusion chem

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The regulation of gene expression in eukaryotes: bistability and oscillations in repressilator models

Rui DILãO

To model the regulation of gene expression in eukaryotes by transcriptional activators and repressors, we introduce delays in conjugation with the mass action law. Delays are associated with the time gap between the mRNA transcription in the nucle

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Noyaux du transfert automorphe de Langlands et formules de Poisson non linéaires: Notes de cours

Laurent LAFFORGUE

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On weakly group-theoretical non-degenerate braided fusion categories

Sonia NATALE

We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to s

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Special Functions in Minimal Representations

Toshiyuki KOBAYASHI

Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal representations.

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Rankin-Cohen Operators for Symmetric Pairs

Toshiyuki KOBAYASHI, Michael PEVZNER

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Sur la correspondance de Simpson p-adique. II : aspects globaux

Ahmed ABBES, Michel GROS

We develop a new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0. This second article is devoted to the global

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Sur la correspondance de Simpson p-adique. 0 : une vue d'ensemble

Ahmed ABBES, Michel GROS

We develop a new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0. The aim of this article is to give an extensi

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F-method for constructing equivariant differential operators

Toshiyuki KOBAYASHI

Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to

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Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring

Sarp AKCAY, Leor BARACK, Thibault DAMOUR, Norichika SAGO

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Gravitational radiation reaction along general orbits in the effective one-body formalism

Donato BINI, Thibault DAMOUR

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Minkowski Measurability Results for Self-Similar Tilings and Fractals with Monophase Generators

Michel L. LAPIDUS, Erin P. J. PEARSE, Steffen WINTER

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Dirac Operators and Geodesic Metric on the Harmonic Sierpinski Gasket and Other Fractal Sets

Michel L. LAPIDUS, Jonathan J. SARHAD

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The Decimation Method for Laplacians on Fractals: Spectra and Complex Dynamics

Nishu LAL, Michel L. LAPIDUS

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Towards an axiomatic geometry of fundamental interactions in noncommutative space-time at Planck scale

Arthemy KISELEV

We outline an axiomatic quantum picture unifying the four fundamental interactions; this is done by exploring a possible physical meaning of the notions, structures, and logic in a class of noncommutative geometries which has been introduced in [IHES/

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Temperedness of Reductive Homogeneous Spaces

Yves BENOIST, Toshiyuki KOBAYASHI

Let G be a semisimple algebraic Lie group and H a reductive subgroup. We compute geometrically the best even integer p for which the representation of G in L^2(G/H) is almost L^p. As an application, we give a criterion which detects whether this repr

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Noyaux du transfert automorphe de Langlands et formules de Poisson non lin\'eaires

Laurent LAFFORGUE

On montre qu'un certain type de formules de Poisson non lin'eaires explicites, qui est impliqu'e par le principe de fonctorialit'e de Langlands, permet de construire des ``noyaux'' du transfert automorphe. Il y a donc 'equivalence entre le principe

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The Current State of Fractal Billiards

Michel L. LAPIDUS, Robert G. NIEMEYER

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Varna Lecture on $L^2$-Analysis of Minimal Representations

Toshiyuki KOBAYASHI

Minimal representations of a real reductive group G are the 'smallest' irreducible unitary representations of G. The author suggests a program of global analysis built on minimal representations from the philosophy: 'small' representatio

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Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator

Hafedh HERICHI, Michel L. LAPIDUS

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Discrete Spectrum for non-Riemannian Locally Symmetric Spaces --- I. Construction and Stability

Fanny KASSEL, Toshiyuki KOBAYASHI

We study the discrete spectrum of the Laplacian on certain pseudo-Riemannian manifolds M which are quotients of reductive symmetric spaces X by discrete groups of isometries acting properly discontinuously. Assuming that X admits a maximal compact subsym

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Minkowski Measurability and Exact Fractal Tube Formulas for p-Adic Self-Similar Strings

Michel L. LAPIDUS, Hung LU, Machiel VAN FRANKENHUIJSEN

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One-Loop four-graviton amplitudes in N=4 supergravity models

Piotr TOURKINE, Pierre VANHOVE

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The zero locus of the infinitesimal invariant

Gregory PEARLSTEIN, Christian SCHNELL

Let $\nu$ be a normal function on a complex manifold $X$. The infinitesimal invariant of $\nu$ has a well-defined zero locus inside the tangent bundle $TX$. When $X$ is quasi-projective, and $\nu$ is admissible, we show that this zero locus

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Box-Counting Fractal Strings, Zeta Functions, and Equivalent Forms of Minkowski Dimension

Michel L. LAPIDUS, John A. ROCK, Darko ZUBRINIC

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Multifractal Analysis via Scaling Zeta Functions and Recursive Structure of Lattice Strings

Rolando DE SANTIAGO, Michel L. LAPIDUS, Scott A. ROBY, John A. ROCK

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On dimension growth of groups

Alexander DRANISHNIKOV, Mark SAPIR

The (asymptotic) dimension growth functions of groups were introduced by Gromov in 1999. In this paper, we show connections between dimension growth and expansion properties of graphs, Ramsey theory and the Kolmogorov-Ostrand dimension of groups an

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Sequences of Compatible Periodic Hybrid Orbits of Prefractal Koch Snowflake Billiards

Michel L. LAPIDUS, Robert G. NIEMEYER

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Partition Zeta Functions, Multifractal Spectra, and Tapestries of Complex Dimensions

Kate E. ELLIS, Michel L. LAPIDUS, Michael C. MACKENZIE, John A. ROCK

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The twelve lectures in the (non)commutative geometry of differential equations

Arthemy KISELEV

These notes follow the twelve-lecture course in the geometry of nonlinear partial differential equations of mathematical physics. Briefly yet systematically, we outline the geometric and algebraic structures associated with such equations and study the pr

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Hyperfunctions and Spectral Zeta Functions of Laplacians on Self-Similar Fractals

Nishu LAL, Michel L. LAPIDUS

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Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description

Donato BINI, Thibault DAMOUR, Guillaume FAYE

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Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals

Thibault DAMOUR, Alessandro NAGAR, Loic VILLAIN

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Riemann Zeroes and Phase Transitions via the Spectral Operator on Fractal Strings

Hafedh HERICHI, Michel L. LAPIDUS

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Gravity, strings, modular and quasimodular forms

P. Mario PETROPOULOS, Pierre VANHOVE

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On the Tutte-Krushkal-Renardy polynomial for cell complexes

Carlos BAJO, Bradley BURDICK, Sergei CHMUTOV

Recently V.Krushkal and D.Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A.~Duval, C.~Klivans, and J.~Martin. Moreov

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Hopf Galois (Co)Extensions In Noncommutative Geometry

Mohammad HASSANZADEH

We introduce an alternative proof, with the use of tools and notions for Hopf algebras, to show that Hopf Galois coextensions of coalgebras are the sources of stable anti Yetter-Drinfeld modules. Furthermore we show that two natural cohomology theories re

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Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems

Joel LEBOWITZ, David RUELLE, Eugene SPEER

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On Generalizations of Connes-Moscovici Characteristic Map

Mohammad HASSANZADEH

In this paper we generalize the Connes-Moscovici characteristic map for cyclic cohomology of extended version of Hopf algebras called x-Hopf algebras. To do this, we define a pairing for cyclic cohomology of module algebras and module coalgebras

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Algebras for Amplitudes

N.E.J. BJERRUM-BOHR, P.H. DAMGAARD, R. MONTEIRO, D. O'CONNELL

Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in gauge theory am

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A $R^4$ non-renormalisation theorem in ${\mathcal N} = 4$ supergravity

Piotr TOURKINE, Pierre VANHOVE

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Quantization is a mystery

Ivan TODOROV

Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students who have had a first course in quantum mechanics). After recall

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Spatial variation of fundamental couplings and Lunar Laser Ranging

Thibault DAMOUR, John F. DONOGHUE

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Energy versus Angular Momentum in Black Hole Binaries

T. DAMOUR, A. NAGAR, D. POLLNEY, C. REISSWIG

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History of Mathematics from a working mathematician's view

Michael MONASTYRSKY

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SMALL REPRESENTATIONS, STRING INSTANTONS, AND FOURIER MODES OF EISENSTEIN SERIES

M.B. GREEN, S.D. MILLER, P. VANHOVE

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A Juzvinski\u{i} Addition Theorem for Finitely Generated Free Groups Actions

Lewis BOWEN, Yonatan GUTMAN

The classical Juzvinski\u{i} Addition Theorem states that the entropy of an automorphism of a compact group decomposes along invariant subgroups. Thomas generalized the theorem to a skew-product setting. Using L. Bowen's f-invariant we prove th

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Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

A.V. KISELEV

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Symplectic structures on moduli spaces of framed sheaves on surfaces

Francesco SALA

We provide generalizations of the notions of Atiyah class and the Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we de ne a symplec

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N=4 SYM Regge Amplitudes and Minimal Surfaces in AdS/CFT Correspondence

Matteo GIORDANO, Robi PESCHANSKI, Shigenori SEKI

The high-energy behavior of N=4 SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. For massless gluon-gluon scattering, we consider the amplitude found by Alday and Maldacena using a minimal surface in $AdS_5$

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The growth rate of symplectic Floer homology

Alexander FEL'SHTYN

The main theme of this paper is to study for a symplectomorphism of a compact surface, the asymptotic invariant which is defined to be the growth rate of the sequence of the total dimensions of symplectic Floer homologies of the iterates of the symplectom

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Collapsing of Abelian Fibred Calabi-Yau Manifolds

Mark GROSS, Valentino TOSATTI, Yuguang ZHANG

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Topos co-évanescents et généralisations

Ahmed ABBES, Michel GROS

Cet article est consacré à l'étude d'un topos introduit par Faltings pour les besoins de la théorie de Hodge $p$-adique. Nous en présentons une nouvelle approche basée sur une généralisation des topos co-évanescents de Deligne. Chemin faisant,

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Surjectivity and equidistribution of the word $x^ay^b$ on $PSL(2,q)$ and $SL(2,q)$

Tatiana BANDMAN, Shelly GARION

We determine the positive integers a,b and the prime powers q for which the word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We moreover show that this map is almost equidistributed for the family of groups PSL(2,q) (and SL(2,q)).

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From Traditional Set Theory -- that of Cantor, Hilbert, G\"odel, Cohen -- to Its Necessary Quantum Extension

Edouard BELAGA

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The vanishing volume of D=4 superspace

G. BOSSARD, P.S. HOWE, K.S. STELLE, P. VANHOVE

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Darboux coordinates, Yang-Yang functional, and gauge theory

N. NEKRASOV, A. ROSLY, S. SHATASHVILI

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Tempered automorphic representations of the unitary group

Paul-James WHITE

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of Arthur's descri

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How to take advantage of the blur between the finite and the infinite

Pierre CARTIER

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Derived equivalences for cluster-tilted algebras of Dynkin type D

Janine BASTIAN, Thorsten HOLM, Sefi LADKANI

We provide a far reaching derived equivalence classification of cluster-tilted algebras of Dynkin type D. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmicall

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Mutation classes of certain quivers with potentials as derived equivalence classes

Sefi LADKANI

We characterize the marked bordered unpunctured oriented surfaces with the property that all the Jacobian algebras of the quivers with potentials arising from their triangulations are derived equivalent. These are either surfaces of genus g with b boundar

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Which mutation classes of quivers have constant number of arrows?

Sefi LADKANI

We classify the connected quivers with the property that all the quivers in their mutation class have the same number of arrows. These are the ones having at most two vertices, or the ones arising from triangulations of marked bordered oriented surfaces o

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Multiscale analysis of biological functions: the example of biofilms

Annick LESNE

Biological functions involve processes at different scales. This statement is obviously true for organismic processes like development. It is already relevant for a bacterial colony, the example on which we shall more specifically focus here. Understandin

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Configuration Space Renormalization of Massless QFT as an Extension Problem for Associate Homogeneous Distributions

Nikolay M. NIKOLOV, Raymond STORA, Ivan TODOROV

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Quantum Einstein-Dirac Bianchi Universes

Thibault DAMOUR, Philippe SPINDEL

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Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models

Luca BAIOTTI, Thibault DAMOUR, Bruno GIACOMAZZO, Alessandro NAGAR, Luciano REZZOLLA

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Sur la correspondance de Simpson p-adique. I : étude locale

Ahmed ABBES, Michel GROS

Nous développons une nouvelle approche pour la correspondance de Simpson p-adique, intimement liée à l'approche originelle de Faltings, mais aussi inspirée du travail d'Ogus et Vologodsky sur un analogue en caractéristique p>0. Ce premi

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On Vassiliev invariants of braid groups of the sphere

Nizar KAABI, Vladimir VERSHININ

We construct a universal Vassiliev invariant for braid groups of the sphere and the mapping class groups of the sphere with $n$ punctures. The case of a sphere is different from the classical braid groups or braids of oriented surfaces of genus st

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Shannon entropy: a rigorous mathematical notion at the crossroads between probability, information theory, dynamical systems and statistical physics

Annick LESNE

Statistical entropy was introduced by Shannon as a basic concept in information theory, measuring the average missing information on a random source. Extended into an entropy rate, it gives bounds in coding and compression theorems. I here present how

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On finite arithmetic groups

Dmitry MALININ

In this paper we study representations of finite groups stable under Galois operation over arithmetic rings in local and global fields.

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On localization in holomorphic equivariant cohomology

Ugo BRUZZO, Vladimir RUBTSOV

We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. localization formula.

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Statistical Properties of Cosmological Billiards

Thibault DAMOUR, Orchidea LECIAN

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On Effective Action of Multiple M5-branes and ABJM Action

Seiji TERASHIMA, Futoshi YAGI

We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which we found in the previous paper. We obtain D4-brane-like action but the gauge coupling constant depends on the spacetime coordinate. This is consistent with th

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Cyclic structures in algebraic (co)homology theories

Niels KOWALZIG, Ulrich KRAEHMER

This note discusses the cyclic cohomology of a left Hopf algebroid ($\times_A$-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and M

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Generalized matrix models and AGT correspondence at all genera

Giulio BONELLI, Kazunobu MARUYOSHI, Alessandro TANZINI, Futoshi YAGI

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams.

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Incompressibility of generic orthogonal grassmannians

Nikita KARPENKO

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A uniqueness theorem for meromorphic mappings with two families of hyperplanes

Gerd DETHLOFF, Duc Quang SI, Van Tan TRAN

In this paper, we extend the uniqueness theorem for meromorphic mappings to the case where the family of hyperplanes depends on the meromorphic mapping and where the meromorphic mappings may be degenerate.

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TENSOR STRUCTURE FROM SCALAR FEYNMAN MATROIDS

Dirk KREIMER, Karen YEATS

We show how to interpret the scalar Feynman integrals which appear when reducing tensor integrals as scalar Feynman integrals coming from certain nice matroids.

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Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism

Leor BARACK, Thibault DAMOUR, Norichika SAGO

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Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars

Luca BAIOTTI, Thibault DAMOUR, Bruno GIACOMAZZO, Alessandro NAGAR, Luciano REZZOLLA

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Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries

Thibault DAMOUR, Miquel TRIAS, Alessandro NAGAR

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Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces

Kwokwai CHAN, Siu-Cheong LAU

We compute the open Gromov-Witten invariants for every compact semi-Fano toric surface, i.e. a toric surface $X$ with nef anticanonical bundle. Unlike the Fano case, this involves non-trivial obstructions in the corresponding moduli problem. As an

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The momentum kernel of gauge and gravity theories

N.E.J. BJERRUM-BOHR, P.H. DAMGAARD, T. SONDERGAARD, P. VANHOVE

We derive an explicit formula for factorizing an n-point closed string amplitude into open string amplitudes. Our results are phrased in terms of a momentum kernel which in the limit of infinite string tension reduces to the corresponding field theo

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Highly Transitive Actions of Out(Fn)

Shelly GARION, Yair GLASNER

An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n>3 the group Out(Fn) = Aut(Fn)/Inn(Fn) admits a faithful highly transitive action on a

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Seiberg-Witten curve via generalized matrix model

Kazunobu MARUYOSHI, Futoshi YAGI

We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N=2 SU(2)^n gauge theory with circular quiver diagram by the AGT relation. We first verify that it is obtained from the

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Geometric analysis on small representations of GL(N,R)

Toshiyuki KOBAYASHI, Bent OERSTED, Michael PEVZNER

The most degenerate unitary principal series representations \pi_{i\lambda,\delta} (\lambda \in R, \delta \in Z/2 Z) of G = GL(N,R) attain the minimum of the Gelfand--Kirillov dimension among all irreducible unitary representations of G. This

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On the Surjectivity of Engel Words on PSL(2,q)

Tatiana BANDMAN, Shelly GARION, Fritz GRUNEWALD

We investigate the surjectivity of the word map defined by the n-th Engel word on the groups PSL(2,q) and SL(2,q). For SL(2,q), we show that this map is surjective onto the subset SL(2,q)\{-id} provided that q>Q(n) is sufficiently large. Moreove

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a-Maximization in N=1 Supersymmetric Spin(10) Gauge Theories

Teruhiko KAWANO, Futoshi YAGI

A summary is reported on our previous publications about four dimensional N=1 supersymmetric Spin(10) gauge theory with chiral superfields in the spinor and vector representations in the non-Abelian Coulomb phase. Carrying out the method of \amax

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Topological invariants and moduli spaces of Gorenstein quasi-homogeneous surface singularities.

Sergey NATANZON, Anna PRATOUSSEVITCH

We describe all connected components of the space of hyperbolic Gorenstein quasi-homogeneous surface singularities. We prove that any connected component is homeomorphic to a quotient of Rd by a discrete group.

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Restrictions of generalized Verma modules to symmetric pairs

Toshiyuki KOBAYASHI

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to reductive symmetric pairs (g, g'). In general, Verma modules may not contain any simple module when restricted to a reductive subalgebra. In th

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Ramification and cleanliness

Ahmed ABBES, Takeshi SAITO

This article is devoted to studying the ramification of Galois torsors and of $\ell$-adic sheaves in characteristic $p>0$ (with $\ell\not=p$). Let $k$ be a perfect field of characteristic $p>0$, $X$ be a smooth, separated and quasi-compact $k$-scheme,

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Noncommutative Toda Chains, Hankel quasideterminants and Painlev\'e II equation

Vladimir RETAKH, Vladimir RUBTSOV

We construct solutions of an infinite Toda system and an analogue of Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.

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Global Stringy Orbifold Cohomology, K-theory and de Rham Theory

Ralph KAUFMANN

There are two approaches to constructing stringy multiplications for global quotients. The first one is given by first pulling back and then pushing forward. This has been used to define a global stringy extension of the functors $K_0,K^{top},

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Phenomenology of the Equivalence Principle with Light Scalars

Thibault DAMOUR, John F. DONOGHUE

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Equivalence Principle Violations and Couplings of a Light Dilaton

Thibault DAMOUR, John F. DONOGHUE

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Categorification of the Jones-Wenzl Projectors

Benjamin COOPER, Vyacheslav KRUSHKAL

The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes, whose graded Euler characteristic is the ``classical''p

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FEYNMAN AMPLITUDES AND LANDAU SINGULARITIES FOR 1-LOOP GRAPHS

Spencer BLOCH, Dirk KREIMER

We use mixed Hodge structures to investigate Feynman amplitudes as functions of external momenta and masses.

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Algebraic Structures in local QFT

Dirk KREIMER

A review of the Hodge and Hopf-algebraic approach to QFT.

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Instantons on Gravitons

Sergey CHERKIS

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF

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Remarks on some locally Qp-analytic representations of GL2(F) in the crystalline case

Christophe BREUIL

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Classical analog of quantum Schwarzschild black hole: local vs global, and the mystery of log 3

Victor BEREZIN

The model is built in which the main global properties of classical and quasi-classical black holes become local. These are the event horizon, no-hair, temperature and entropy. Our construction is based on the features of a quantum collapse, discovered wh

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A Non-differentiable Noether's theorem

Jacky CRESSON, Isabelle GREFF

In the framework of the non-differentiable embedding of Lagrangian systems, defined by Cresson and Greff, we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.

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The critical ultraviolet behaviour of N=8 supergravity amplitudes

Pierre VANHOVE

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Eisenstein series for higher-rank groups and string theory amplitudes

M.B. GREEN, S.D. MILLER, J.G. RUSSO, P. VANHOVE

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Kramers-Wannier Duality for Non-Abelian Lattice Spin Systems and Hecke Surfaces

Michael MONASTYRSKY

We discuss two themes: 1.Duality transformation for generalized Potts models and Hecke surfaces and $K$-regular graphs

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Pseudogroupes de Lie et théorie de Galois différentielle

Bernard MALGRANGE

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Intersecting D4-branes Model of Holographic QCD and Tachyon Condensation

Shigenori SEKI

We consider the intersecting D4-brane and anti-D4-brane model of holographic QCD, motivated by the model that has recently been suggested by Van Raamsdonk and Whyte. We analyze such D4-branes by the use of the tachyonic Dirac-Born-Infeld action, so that w

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Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes

N.E.J BJERRUM-BOHR, Poul DAMGAARD, Thomas SONDERGAARD, Pierre VANHOVE

We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The J

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Monodromy and Kawai-Lewellen-Tye Relations for Gravity Amplitudes

N.E.J. BJERRUM-BOHR, Pierre VANHOVE

🟢-En ligne

A matrix model for the topological string I: deriving the matrix model

Bertrand EYNARD, Amir-Kian KASHANI-POOR, Olivier MARCHAL

🟢-En ligne

String theory dualities and supergravity divergences

Michael B. GREEN, Jorge G. RUSSO, Pierre VANHOVE

🟢-En ligne

Single-Lifting Macaulay-Type Formulae of Generalized Unmixed Toric Resultants

Ioannis EMIRIS, Christos KONAXIS

🟢-En ligne

Minimal representations and reductive dual pairs in conformal field theory

Ivan TODOROV

🟢-En ligne

Automorphic properties of low energy string amplitudes in various dimensions

Michael GREEN, Jorge RUSSO, Pierre VANHOVE

🟢-En ligne

On the ultraviolet behaviour of N=8 supergravity amplitudes

Pierre VANHOVE

🟢-En ligne

Sugawara-type constraints in hyperbolic coset models

Thibault DAMOUR, Axel KLEINSCHMIDT, Hermann NICOLAI

🟢-En ligne

$E_{7(7)}$ invariant Lagrangian of $d=4$ ${\mathcal N} = 8$ supergravity

Christian HILLMANN

🟢-En ligne

Crystal melting on toric surfaces

Michele CIRAFICI, Amir-Kian KASHANI-POOR, Richard SZABO

🟢-En ligne

Almost etale resolution of foliations

Michael MCQUILLAN, Daniel PANAZZOLO

🟢-En ligne

La cosmologie: un laboratoire pour la théorie des cordes

Pierre VANHOVE

🟢-En ligne

Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism

Thibault DAMOUR

🟢-En ligne

Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries

Thibault DAMOUR, Bala R. IYER, Alessandro NAGAR

🟢-En ligne

Sur un problème de compatibilité local-global modulo p pour GL2

Christophe BREUIL

🟢-En ligne

Construire un noyau de la fonctorialité~? \\ Le cas de l'induction automorphe \\ sans ramification de ${\rm GL}_1$ à ${\rm GL}_2$

Laurent LAFFORGUE

Le but de cet article (à paraître aux Annales de l'Institut Fourier) est de présenter une nouvelle méthode purement adélique pour réaliser le principe de fonctorialité de Langlands dans le cas de l'induction automorphe sans ramification de GL(1) à GL(2)

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Construire des noyaux de la fonctorialité~? \\ Définition générale, \\ cas de l'identité de ${\rm GL}_2$ \\ et construction générale conjecturale \\ de leurs coefficients de Fourier

Laurent LAFFORGUE

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Notes sur l'histoire et la philosophie des mathématiques V : le problème de l'espace

Pierre CARTIER

🟢-En ligne

Noncommutative $\mathbf{K}$-correspondence categories, simplicial sets and pro $C^*$-algebras

Snigdhayan MAHANTA

🟢-En ligne

A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle

Tyler JARVIS, Takashi KIMURA

🟢-En ligne

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

Nathan BERKOVITS, Michael B. GREEN, Jorge G. RUSSO, Pierre VANHOVE

🟢-En ligne

Living in a contradictory world: categories vs sets?

Pierre CARTIER

🟢-En ligne

RENORMALIZATION AND RESOLUTION OF SINGULARITIES

Christoph BERGBAUER, Romeo BRUNETTI, Dirk KREIMER

🟢-En ligne

Minimal Basis for Gauge Theory Amplitudes

N.E.J. BJERRUM-BOHR, Poul DAMGAARD, Pierre VANHOVE

🟢-En ligne

Vinberg Algebras and Combinatorics

Pierre CARTIER

Vinberg algebras are usually called pre-Lie algebras and were introduced long ago by Gerstenhaber. We propose to follow a di&#64256;erent route by motivating these algebras by problems coming from di&#64256;erential geometry, and &#64257;rst studi

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On the gravitational polarizability of black holes

Thibault DAMOUR, Orchidea maria LECIAN

🟢-En ligne

Fermionic Kac-Moody Billiards and Supergravity

Thibault DAMOUR, Christian HILLMANN

🟢-En ligne

Supersymmetric Vacua and Bethe Ansatz

Nikita NEKRASOV, Samson SHATASHVILI

🟢-En ligne

The Effective One Body description of the Two-Body problem

Thibault DAMOUR, Alessandro NAGAR

🟢-En ligne

Relativistic tidal properties of neutron stars

Thibault DAMOUR, Alessandro NAGAR

🟢-En ligne

An improved analytical description of inspiralling and coalescing black-hole binaries

Thibault DAMOUR, Alessandro NAGAR

🟢-En ligne

Simplicity of Amplitudes in Gravity and Yang-Mills Theories

N.E.J. BJERRUM-BOHR, Pierre VANHOVE

🟢-En ligne

Algebras for quantum fields

Dirk KREIMER

We give an account of the current state of the approach to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic structures he

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The QCD $\beta$-function from global solutions to Dyson-Schwinger equations

Guillaume VAN BAALEN, Dirk KREIMER, David UMINSKY, Karen YEATS

We study quantum chromodynamics from the viewpoint of untruncated Dyson–Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is unknown b

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The Big Bang as the Ultimate Traffic Jam

Vishnu JEJJALA, Michael KAVIC, Djordje MINIC, Chia-hsiung TZE

We present a novel solution to the nature and formation of the initial state of the Universe. It derives from the physics of a generally covariant extension of Matrix theory. We focus on the dynamical state space of this background independent quan

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Surprising simplicity of N=8 supergravity

Emil BJERRUM-BOHR, Pierre VANHOVE

🟢-En ligne

An infinite family of solvable and integrable quantum systems on a plane

Frederick TREMBLAY, Alexander TURBINER, Pavel WINTERNITZ

An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of thisf

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Quantum Groups and Braid Group Statistics in Conformal Current Algebra Models

Ivan TODOROV, Ludmil HADJIIVANOV

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Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence

Leonid POSITSELSKI

We discuss derived categories of the first kind for DG-modules, DG-comodules, and DG-contramodules, derived categories of the second kind for CDG-modules, CDG-comodules, and CDG-contramodules. For the latter two, the comodule-contramodule correspondenc

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Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles

Dmitri PANYUSHEV

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Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariable Polynomials. II. $E_7$ case

J.c. LOPEZ, M.a.g. GARCIA, A.v. TURBINER

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Discrete Minimal Surface Algebras

Joakim ARNLIND, Jens HOPPE

We consider Discrete Minimal Surface Algebras (DMSA) as noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in the context of Membrane Theory, where sequences of their representations are used as a r

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Higher-loop amplitudes in the non-minimal pure spinor formalism

Pietro GRASSI, Pierre VANHOVE

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Recursive relations in the core Hopf algebra

Dirk KREIMER, Walter VAN SUIJLEKOM

We study co-ideals in the core Hopf algebra underlying a quantum field theory.

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Integrable Systems in Noncommutative Spaces

Masashi HAMANAKA

We discuss extension of soliton theories and integrable systems into non-commutative (NC) spaces. In the framework of NC integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many NC integrable equations,

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Scattering Amplitudes and BCFW Recursion in Twistor Space

Lionel MASON, David SKINNER

A number of recent advances in our understanding of scattering amplitudes have been inspired by ideas from twistor theory. While there has been much work studying the twistor space support of scattering amplitudes, this has largely been done by examiningt

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An accurate few-parameter ground state wave function for the Lithium atom

Nicolais GUEVARA, Frank HARRIS, Alexander TURBINER

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On two-dimensional quantum gravity and quasiclassical integrable hierarchies

Andrei MARSHAKOV

🟢-En ligne

Essential hyperbolic Coxeter polytopes

Anna FELIKSON, Pavel TUMARKIN

We introduce a notion of essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We de

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The core Hopf algebra

Dirk KREIMER

We study the core Hopf algebra underlying the renormalization Hopf algebra.

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On a class of hamiltonian fiber bundles

Aleksy TRALLE, Jarek KEDRA, Anna SZCZEPKOWSKA

We study an interesting class of hamiltonian fiber bundles whose fibers are compact homogeneous symplectic manifolds. Applications to the cohomology of their symplectomorphism group are given.

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Exploiting N=2 in consistent coset reductions of type IIA

Davide CASSANI, Amir-kian KASHANI-POOR

🟢-En ligne

Generalized E(7(7)) coset dynamics and D=11 supergravity

Christian HILLMANN

The hidden on-shell E(7(7)) symmetry of maximal supergravity is usually discussed in a truncation from D=11 to four dimensions. In this article, we reverse the logic and start from a theory with manifest off-shell E(7(7)) symmetry inspired by West's cose

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Un pays dont on ne connaîtrait que le nom (Grothendieck et les 'motifs')

Pierre CARTIER

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Topological String on ${\mathcal S}^2$ Revisited

Alexander ALEXANDROV, Nikita NEKRASOV

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Théories de Galois géométriques

Pierre CARTIER

Nous présentons de manière conceptuelle les idées de Riemann sur les singularités et la monodromie, et nous l'illustrons par l'étude des fonctions algébriques, et des solutions des équations différentielles. Cela fournit une approche unifiée aux diverse

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Yet Another Poincaré's Polyhedron Theorem

Sasha ANAN'IN, Carlos GROSSI

This work contains a new version of Poincare's Polyhedron Theorem that also suits geometries of nonconstant curvature lacking concepts of convexity. Most conditions of the theorem, being as local as possible, are easy to verify in practice.

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Notion de spectre

Pierre CARTIER

La notion de spectre est au départ une notion physique. Elle a pris progressivement une signification de plus en plus large en mathématique, sa signification mathématique la plus importante lui ayant été donnée par Grothendieck dans sa théorie des schémas

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Entropy estimation of symbolic sequences: How short is a short sequence?

Annick LESNE, Jean-luc BLANC, Laurent PEZARD

While entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series, its estimation is often hampered by the finite length of the data. We here investigate the performance of entropy estimation procedures, re

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Quantum Integrability and Supersymmetric Vacua

Nikita NEKRASOV, Samson SHATASHVILI

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Phase space polarization and the topological string: a case study

Amir-Kian KASHANI-POOR

🟢-En ligne

About Time

Vishnu JEJJALA, Michael KAVIC, Djordje MINIC, Chia-Hsiung TZE

🟢-En ligne

Simplicity in the Structure of QED and Gravity Amplitudes

Simon BADGER, Niels Emil Jannik BJERRUM-BOHR, Pierre VANHOVE

🟢-En ligne

Dimensional Regularization of the Gravitational Interaction of Point Masses in the ADM Formalism

T. DAMOUR, P. JARANOWSKI, G. SCHAEFER

🟢-En ligne

Improved Resummation of Post-Newtonian Multipolar Waveforms from Circularized Compact Binaries

T. DAMOUR, B.R. IYER, A. NAGAR

🟢-En ligne

Two Dimensional Topological Strings and Gauge Theory

Nikita A. NEKRASOV

🟢-En ligne

Multi-valued hyperelliptic continued fractions of generalized Halphen type

Vladimir DRAGOVIC

We introduce and study higher genera generalizations of the Halphen theory of continued fractions. The basic notion we start with is hyperel- liptic Halphen (HH) element p X2g+2 ¡ p Y2g+2 x ¡ y ; depending on parameter y, where X2g+2 is a polynom

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Partition Functions of Matrix Models as the First Special Functions of String Theory II. Kontsevich Model

A. ALEXANDROV, A. MIRONOV, A. MOROZOV, P. PUTROV

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Diagrammes de Diamond et $(\varphi,\Gamma)$-modules

Christophe BREUIL

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Piecewise principal comodule algebras

P.M. HAJAC, U. KRAHMER, R. MATTHES, B. ZIELINSKI

A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality is a pie

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Tamagawa defect of Euler systems

Kazim BUYUKBODUK

As remarked by Mazur an Rubin (2004, {\em Mem. Amer. Math. Soc.\/}, 168(799)) one does not expect the Kolyvagin system obtained from an Euler system for a $p$-adic Galois representation $T$ to be \emph{primitive} (in the sense of \emph{loc. cit.}) if$

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Stickelberger elements and Kolyvagin systems

Kazim BUYUKBODUK

In this paper we construct (many) Kolyvagin systems out of Stickelberger elements, utilizing ideas borrowed from our previous work on Kolyvagin systems of Stark elements. We show how to apply this construction to prove results on the \emph{odd} parts oft

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Vertex algebroids over Veronese rings

Fyodor MALIKOV

We find a canonical quantization of Courant algebroids over Veronese rings. Part of our approach allows a semi-infinite cohomology interpretation, and the latter can be used to define sheaves of chiral differential operators on some homogeneous spaces

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LOCAL STABILITY OF A QUASI-LINEAR AGE-SIZE STRUCTURED POPULATION DYNAMICS MODEL

Jean TCHUENCHE

The local stability of a quasi-linear age-size structured population model studied in Tchuenche (2007) is analysed. If a certain threshold parameter known as the basic reproductive rate is less than unity, then the trivial steady state is locally asymptot

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Pure Spinor Partition Function and the Massive Superstring Spectrum

Y. AISAKA, E.A. ARROYO, N. BERKOVITS, N. NEKRASOV

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One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model

Joseph BEN GELOUN, Adrian TANASA

Recently, a new type of renormalizable $\phi^{\star 4}_{4}$ scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a $a/(\theta^2p^2)$ term. We calculate here the$

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SELF-SIMILAR P-ADIC FRACTAL STRINGS AND THEIR COMPLEX DIMENSIONS

Michel LAPIDUS, Lu HUNG

We develop a geometric theory of self-similar p-adic fractal strings and their complex dimensions. We obtain a closed-form formula for the geo- metric zeta functions and show that these zeta functions are rational functions in an appropriate variabl

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Regularization, renormalization, and renormalization groups: relationships and epistemological aspects

Annick LESNE

This paper confronts renormalization used in quantum field theory and that used in critical phenomena studies in statistical mechanics or dynamical systems theory. Regularization that cures spurious divergences is distinguished from renormalization t

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Open-Closed Moduli Spaces and Related Algebraic Structures

Eric HARRELSON, Alexander A. VORONOV, J. Javier ZUNIGA

We set up a Batalin-Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological s

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A trace on fractal graphs and the Ihara zeta function

Daniele GUIDO, Tommaso ISOLA, Michel LAPIDUS

Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and Terras, Mizuno and Sato, to name just a few authors. Then, Clair and Mokhtari-Sha

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Ihara's zeta function for periodic graphs and its approximation in the amenable case

Daniele GUIDO, Tommaso ISOLA, Michel LAPIDUS

In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi on the zeta functions of periodic graphs. In particular, using appropriate operator-algebraic techniques, we establish a determinant formula in th

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Bartholdi Zeta Functions for Periodic Simple Graphs

Daniele GUIDO, Tommaso ISOLA, Michel LAPIDUS

The definition of the Bartholdi zeta function is extended to the case of infinite periodic graphs. By means of the analytic determinant for semifinite von~Neumann algebras studied by the authors in \cite{GILa03}, a determinant formula and funct

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Ihara zeta functions for periodic simple graphs

Daniele GUIDO, Tommaso ISOLA, Michel LAPIDUS

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by S

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Toward zeta functions and Complex Dimensions of Multifractals

Michel LAPIDUS, John ROCK

Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry, spectra and dy

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Turbulence and Holography

Vishnu JEJJALA, Djordje MINIC, Y. Jack NG, Chia-Hsiung TZE

🟢-En ligne

Sutherland-type trigonometric models, trigonometric invariants, and multivariate polynomials

Konstantin BORESKOV, Alexander TURBINER, Juan Carlos LOPEZ VIEYRA

🟢-En ligne

The QED $\beta$-function from global solutions to Dyson-Schwinger equations

G. VAN BAALEN, D. KREIMER, D. UMINSKY, K. YEATS

We discuss the structure of beta functions as determined by the recursive nature of Dyson-Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine

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Tube Formulas and complex Dimensions of Self-Similar tilings

Michel L. LAPIDUS, Erin P. J. PEARSE

We use the self-similar tilings constructed by Erin Pearse to define a generating function for the geometry of a self-similar set in Euclidean space. This geometric zeta function encodes scaling and curvature properties related to the complement of th

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Tube Formulas for Self-Similar Fractals

Michel L. LAPIDUS, Erin P. J. PEARSE

Tube formulas (by which we mean an explicit formula for the volume of an (inner) epsilon-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space

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Nonarchimedean Cantor Set and String

Michel L. LAPIDUS, Lu HUNG

We construct a nonarchimedean (or p-adic) analogue of the classical ternary set C. In particular, we show that this nonarchimedean Cantor set C3 is self-similar. Furthermore, we characterize C3 as the subset of 3-adic integers whose elements contain onl

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MIXED HODGE STRUCTURES AND RENORMALIZATION IN PHYSICS

Spencer BLOCH, Dirk KREIMER

We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.

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Recycling the Independent Field Approximation argument in the far field

Konstantinos KARAMANOS

The Independent Field Approximation for the entropy production of Laplacian mild di&#64256;usional &#64257;elds is rigorously introduced and discussed. Some new results due to super-convergent algorithms are presented and the meaning of the active zon

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On the origin of time and the Universe

Vishnu JEJJALA, Michael KAVIC, Djordje MINIC, Hsiung-Chia TZE

🟢-En ligne

Fractal structure of the block-complexity function

Konstantinos KARAMANOS, Ilias KOTSIREAS

We demonstrate that the block-complexity function for words from 3-letter and 4-letter alphabets exhibits a fractal structure. The resulting fractals have dimensions approximately equal to 1.892 and 1.953 respectively. We visualize approximations of the

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Infinite Dimensional Lie Algebras in 4D Conformal Field Theory

Ivan TODOROV

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On a class of holonomic D-modules on symmetric matrices attached to the general linear group

Philibert NANG

We give a classification of regular holonomic D-modules on complex symmetric matrices whose characteristic variety is the union of conormal bundles to the orbits of the general linear group

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Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries

T. DAMOUR, A. NAGAR, M. HANNAM, S. HUSA, B. BRUEGMANN

🟢-En ligne

SQCD: A Geometric Apercu

J. GRAY, A. HANANY, Y.-H. HE, V. JEJJALA, N. MEKAREEYA

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character

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Groupoides de Lie et leurs alg\'ebroides

Pierre CARTIER

Résumé : Ce texte d’un exposé prochain au Séminaire Bourbaki est une revue des notions de géométrie différentielle liées aux variétés symplectiques et de Poisson, aux groupoides de Lie et aux algébroides de Lie. Ces notions ont des liens multiples,et la

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Instantons beyond topological theory II

E. FRENKEL, A. LOSEV, N. NEKRASOV

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On the conjecture of Kevin Walker

Michael FARBER, Jean-Claude HAUSMANN, Dirk SCHUETZ

In 1985 Kevin Walker in his study of topology of polygon spaces raised an interesting conjecture in the spirit of the well-known question "Can you hear the shape of a drum?" of Marc Kac. Roughly, Walker's conjecture asks if one can recover relativel

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Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling

T. DAMOUR, P. JARANOWSKI, G. SCHAEFER

🟢-En ligne

Faithful Effective One Body waveforms of equal-mass coalescing black-hole binaries

T. DAMOUR, A. NAGAR, E.N. DORBAND, D. POLLNEY, L. REZZOLLA

🟢-En ligne

Constraints on the variability of quark masses from nuclear binding

T. DAMOUR, J.F. DONOGHUE

🟢-En ligne

Comparing Effective One Body gravitational waveforms to accurate numerical data

T. DAMOUR, A. NAGAR

🟢-En ligne

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

T. DAMOUR, P. JARANOWSKI, G. SCHAEFER

🟢-En ligne

On the Brownian gas: a field theory with a Poissonian ground state

Andrea VELENICH, Claudio CHAMON, Leticia CUGLIANDOLO, Dirk KREIMER

As a first step towards a successful field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and its nonlinear time-reversal symmetry. Even though the particles do not interact, the field theory c

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NOT SO NON-RENORMALIZABLE GRAVITY

Dirk KREIMER

We review recent ideas [1] how gravity might turn out to be a renormalizable theory after all.

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Quantum Groups and Braid Group Statistics in Conformal Field Theory

Ivan TODOROV

A quantum universal enveloping algebra $U_q$ and the braid group on $n$ strands ${\mathcal B}_n$ mutually commute when acting on the $n$-fold tensor product of a $U_q$-module. Their combined action is applied to low dimensional systems -- the only ones t

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Classical and quantum integrability

Mauricio GARAY, Duco VAN STRATEN

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Cofiniteness conditions, projective covers and the logarithmic tensor product theory

Yi-Zhi HUANG

We construct projective covers of irreducible V-modules in the category of grading-restricted generalized V-modules when V is a vertex operator algebra satisfying the following conditions: 1. V is C_{1}-cofinite in the sense of Li. 2. There existsa

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On the Projective Hull of Certain Curves in $C^2$

F. Reese HARVEY, H. Blaine LAWSON, John WERMER

The projective hull X^ of a compact set X in projective n-space P^n is an analogue of the classical polynomial hull of a set in C^n. In the special case that X lies in an affine chart C^n in P^n, the part of X^ lying in C^n can be defined as th

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Operator-Valued Involutive Distributions of Evolutionary Vector Fields and their Affine Geometry

A.V. KISELEV, J.W. VAN DE LEUR

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Describing general cosmological singularities in Iwasawa variables

Thibault DAMOUR, Sophie DE BUYL

🟢-En ligne

When steric hindrance facilitates processivity: polymerase activity within chromatin

Christophe BECAVIN, Jean-Marc VICTOR, Annick LESNE

During eukaryotic transcription, polymerase activity generates torsional stress in DNA, having a negative impact in polymerase processivity. Using our previous studies of the chromatin fiber structure and conformational transitions, we suggest that this

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Quelques remarques sur le principe de fonctorialit\'e

Laurent LAFFORGUE

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Dirichlet Duality and the Nonlinear Dirichlet Problem

F. Reese HARVEY, H. Blaine LAWSON

We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form f(Hess u)=0 on a smoothly bounded domain D in R^n. In our approach the equation is replaced by a subset F of the space of symmetric nxn-matrices with bd

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Scalar curvature on lightlike hypersurfaces.

Cyriaque ATINDOGBE

In a recent paper by K. Duggal, the concept of induced scalar curvature of lightlike hypersurfaces is introduced, restricting on a specific class of the latter. This paper removes some of these constraints and construct this scalar quantity by an approach

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Deforming, revolving and resolving - New paths in the string theory landscape

Diego CHIALVA, Ulf DANIELSSON, Niklas JOHANSSON, Magdalena LARFORS, Marcel VONK

In this paper we investigate the properties of series of vacua in the string theory landscape. In particular, we study minima to the flux potential in type IIB compactifications on the mirror quintic. Using geometric transitions, we embed its one dime

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The diffeomorphism group of a $K3$ surface and Nielsen realization

Jeffrey GIANSIRACUSA

We use moduli spaces of various geometric structures on a manifold M to probe the cohomology of the diffeomorphism group and mapping class group of M. The general principle is that existence of a moduli problem for which the Teichmuller space resembles ap

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Constraints and the $E_{10}$ Coset Model

T. DAMOUR, A. KLEINSCHMIDT, H. NICOLAI

We continue the study of the one-dimensional $E_{10}$ coset model (massless spinning particlemotion on $E_{10}/K(E_{10}))$ whose dynamics at low levels is known to coincide with the equations of motion of maximal supergravity theories in appropriate trunc

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Restricted set addition: The exceptional case of the Erdos-Heilbronn conjecture

Gyula KAROLYI

Let A,B be different nonempty subsets of the group of integers modulo a prime p. If p is not smaller than |A|+|B|-2, then at least this many residue classes can be represented as a+b, where a and b are different elements of A and B, respectively. This r

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Tubular Neighborhoods of Nodal Sets and Diophantine Approximation

Dmitry JAKOBSON, Dan MANGOUBI

We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on

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Hochschild cohomology, the characteristic morphism and derived deformations

Wendy LOWEN

A notion of Hochschild cohomology of an abelian category was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism from the Hochschild cohomology into the graded centre of the (bounded) derived category. An e

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Towards a modulo $p$ Langlands correspondence for GL$_2$

Christophe BREUIL, Vytautas PASKUNAS

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Subgroup separability in residually free groups

Martin R. BRIDSON, Henry WILTON

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type $FP_\infty$ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of resid

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Perverse coherent sheaves and the geometry of special pieces in the unipotent variety

Pramod ACHAR, Daniel SAGE

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subscheme whose complement has codimension at least 2. We extend the theory of perverse coherent sheaves, due to Deligne and disseminated

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On the derived category of 1-motives, I

Luca BARBIERI VIALE, Bruno KAHN

We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p. As a first result, we provide a fully faithful embedding into an 'etale versio

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A remark on quantum gravity

Dirk KREIMER

We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub Hopf algebra on gravity amplitudes equivalent to identi

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Wormholes as Black Hole Foils

Thibault DAMOUR, Sergey N. SOLODUKHIN

We study to what extent wormholes can mimic the observational features of black holes. It is surprisingly found that many features that could be thought of as 'characteristic' of a black hole (endowed with an event horizon) can be closely mimicked by ag

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Cosmological Singularities and a Conjectured Gravity/Coset Correspondence

Thibault DAMOUR

We review the recently discovered connection between the Belinsky-Khalatnikov-Lifshitz-like "chaotic" structure of generic cosmological singularities in eleven-dimensional supergravity and the "last" hyperbolic Kac-Moody algebra $E_{10}$. This intrigu

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Binary Systems as Test-beds of Gravity Theories

Thibault DAMOUR

We review the general relativistic theory of the motion, and of the timing, of binary systems containing compact objects (neutron stars or black holes). Then we indicate the various ways one can use binary pulsar data to test the strong-field and/or radia

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General Relativity Today

Thibault DAMOUR

After recalling the conceptual foundations and the basic structure of general relativity, we review some of its main modern developments (apart from cosmology): (i) the post-Newtonian limit and weak-field tests in the solar system, (ii) strong-gravitation

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Chaos and Symmetry in String Cosmology

Thibault DAMOUR

We review the recently discovered interplay between chaos and symmetry in the general inhomogeneous solution of many string-related Einstein-matter systems in the vicinity of a cosmological singularity. The Belinsky-Khalatnikov-Lifshitz-type chaotic behav

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Local Asymmetry and the Inner Radius of Nodal Domains

Dan MANGOUBI

Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue lambda. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/lambda^n. Weapp

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B$_{\rm cris}^{\varphi = 1}$-représentations et $(\varphi , \Gamma)$-modules

Laurent BERGER

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The cyclomatic number of connected graphs without solvable orbits

Gyula KAROLYI, Ambrus PAL

A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c if and only if c is equal to 6, 8, 10, 11,

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The Geometry of Small Causal Diamonds

G. W. GIBBONS, S. N. SOLODUKHIN

The geometry of causal diamonds or Alexandrov open sets whose initial and final events $p$ and $q$ respectively have a proper-time separation $ au$ small compared with the curvature scale is a universal. The corrections from flat space are given as

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An $A_{\infty}$-structure for lines in a plane

Hiroshige KAJIURA

As an explicit example of an $A_{\infty}$-structure associated to geometry, we construct an $A_{\infty}$-structure for a Fukaya category of finitely many lines (Lagrangians) in $R^2$, ie., we define also non-transversal $A_{\infty}$-products. This co

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A vanishing theorem in positive characteristic and tilting equivalences

Alexander SAMOKHIN

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Notes on instantons in topological field theory and beyond

E. FRENKEL, A. LOSEV, N. NEKRASOV

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Renormalisation of non-commutative field theories

Vincent RIVASSEAU, Fabien VIGNES-TOURNERET

The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.

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Familles de représentations de De Rham et monodromie p-adique

Laurent BERGER, Pierre COLMEZ

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One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

Ahmed LAKHOUA, Fabien VIGNES-TOURNERET, Jean-Christophe WALLET

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross-Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative fie

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A counterexample to Premet's and Joseph's conjectures

O. YAKIMOVA

Let $g$ be a finite-dimensional reductive Lie algebra of rank $l$ over an algebraically closed field of characteristic zero. Given an element $x$ of $g$, we denote by $g_x$ the centraliser of $x$ in $g$. It was conjectured by Premet, that the algebra

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Lifetime of a massive particle in a de Sitter universe

Jacques BROS, Henri EPSTEIN, Ugo MOSCHELLA

We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so thatd

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Semi-classical open string corrections and symmetric Wilson loops

Satoshi YAMAGUCHI

In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric representation or a multiply wound one in N=4 super Yang-Mills theory. In order to distinguish the sy

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Geometry of differential equations

Boris KRUGLIKOV, Valentin LYCHAGIN

This is a review of classical and modern methods of geometric-algebraic approach to (overdeteremined) systems of partial differential equations.

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Recursion and growth estimates in renormalizable quantum field theory

Dirk KREIMER, Karen YEATS

In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones.

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The next-to-ladder approximation for Dyson-Schwinger equations

Isabella BIERENBAUM, Dirk KREIMER, Stefan WEINZIERL

We solve the linear Dyson Schwinger equation for a massless vertex in Yukawa theory, iterating the first two primitive graphs.

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Extended Seiberg-Witten Theory and Integrable Hierarchy

Andrei MARSHAKOV, Nikita A. NEKRASOV

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Sur un `corps de caractéristique 1' (d'après Zhu)

Paul LESCOT

Nous exposons la théorie de Zhu concernant un analogue formel du corps ${mathbf F}_{p}$, pour `$p=1$'.

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Homotopy graph-complex for configuration and knot spaces

Pascal LAMBRECHTS, Victor TURCHIN

In the paper we prove that the primitive part of the Sinha homology spectral sequence E2-term for the space of long knots is rationally isomorphic to the homotopy E2-term. We also define natural graph-complexes computing the rational homotopy of configu

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Modified Hochschild and Periodic Cyclic Homology

Nicolae TELEMAN

The Hochschild and (periodic) cyclic homology of the algebra of continuous functions on a smooth manifold are trivial. In this paper we create an analogue of the Hochschild and periodic cyclic homology which gives the right result when applied onto

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A generalization of residual finiteness

Daniel TIEUDJO, David MOLDAVANSKII

The concept of residual finiteness with respect to automorphic equivalence, a property generalizing residual finiteness and conjugacy separability is introduced. A sufficient condition for a group G to be residually finite with respect to automorphic eq

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Noncommutative Geometry Approach to Principal and Associated Bundles

P.F. BAUM, P.M. HAJAC, R. MATTHES, W. SZYMANSKI

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The map from the cyclohedron to the associahedron is left cofinal

Pascal LAMBRECHTS, Victor TURCHIN, Ismar VOLIC

Two natural projections from the cyclohedron to the associahedron are defined. We show that the preimages of any point via these projections might not be homeomorphic to (a cell decomposition of) a disc, but are still contractible. We briefly explain ana

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Injectivity Radius of Lorentzian Manifolds

Bing-Long CHEN, Philippe G. LEFLOCH

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Reduction Theorems for characteristic functors on finite $p$-groups and applications to $p$-nilpotence criteria

Paul LESCOT

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Strongly homotopy Lie bialgebras and Lie quasi-bialgebras

Olga KRAVCHENKO

Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras. Cohomology theories of all these structures are descr

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Cardy condition for Open-closed field algebras

Liang KONG

Let $V$ be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $mathcal{C}_V$, the category of $V$-modules, is a modular tensor category. We study open-closed field algebras over $V$ equipped with nondegeneratei

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Field rotation parameters and limit cycle bifurcations

Valery A. GAIKO

In this paper, the global qualitative analysis of planar polynomial dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem on the maximum number and relative position of their limit cycles in two special ca

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Correlator of Fundamental and Anti-symmetric Wilson loops in AdS/CFT Correspondence

Ta-Sheng TAI, Satoshi YAMAGUCHI

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Instantons beyond topological theory I

E. FRENKEL, A. LOSEV, N. NEKRASOV

Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding models as ful

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Open-closed field algebras, operads and tensor categories

Liang KONG

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra $V$. In the case that $V$ satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over $V$ canoni

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Classification of low energy sign-changing solutions of an almost critical problem

Mohamed BEN AYED, Khalil EL MEHDI, Filomena PACELLA

In this paper we make the analysis of the blow-up of low energy sign-changing solutions of a semi-linear elliptic problem involving nearly critical exponent. Our results allow to classify these solutions according to the concentration speeds of the

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Remarks on compact shrinking Ricci solitons of dimension four

Li MA

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A primer of Hopf algebras

Pierre CARTIER

In this paper, we review a number of basic results about so-called Hopf algebras. We begin by giving a historical account of the results obtained in the 1930's and 1940's about the topology of Lie groups and compact symmetric spaces. The climax is provide

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Rigidity theorem for expanding Gradient Ricci Solitons

Li MA

In this paper, we study the rigidity problem for expanding gradient Ricci soliton equation on a complete conformally compact Riemannian manifold. We show that under a natural condition on the Ricci curvature and the scalar curvature, the expanding Ricc

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Linear dependence in Mordell-Weil groups

Wojciech GAJDA, Krzysztof GORNISIEWICZ

We consider a local to global principle for detecting linear dependence of nontorsion points, by reduction maps, in the Mordell-Weil group of an abelian variety defined over a number field.

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A Lie theoretic approach to renormalization

Kurusch EBRAHIMI-FARD, Jose M. GRACIA-BONDIA, Frederic PATRAS

Motivated by recent work of Connes and Marcolli, based on the Connes-Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our results rely both on the properties of the Dynkin idempotent, one of th

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Le Calcul des Probabilités de Poincaré

Pierre CARTIER

Résumé: Le présent texte est extrait d'un ouvrage à paraître sur `L'héritage mathématique de Poincaré' (éditions Belin). Il s'agit d'une analyse du livre de Poincaré sur les probabilités, qui reprend l'un de ses cours, et son texte fameux sur le hasard. L

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Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

Nathan BERKOVITS, Nikita NEKRASOV

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes fromr

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Dessins d'enfants: Solving equations determining Belyi pairs

Elena KREINES

This paper deals with the Grothendieck dessins d'enfants, that is tamely embedded graphs on surfaces. We investigate combinatorics of systems of equations determining corresponding Belyi pair, that is a rational function with at most 3 critical values ona

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Dyson Schwinger Equations: From Hopf algebras to Number Theory

Dirk KREIMER

We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative results for the sh

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Séries hypergéométriques multiples et polyzêtas

Jacky CRESSON, Stephane FISCHLER, Tanguy RIVOAL

Nous décrivons un algorithme théorique et effectif permettant de démontrer que des séries et intégrales hypergéométriques multiples relativement générales se décomposent en combinaisons linéaires à coefficients rationnels de polyzêtas.

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Phénomènes de symétries dans des formes linéaires en polyzêtas

Jacky CRESSON, Stephane FISCHLER, Tanguy RIVOAL

On donne deux généralisations, en profondeur quelconque, du phénomène de symétrie utilisé par Ball-Rivoal pour démontrer qu'une infinité de valeurs de la fonction zeta de Riemann aux entiers impairs sont irrationnelles. Ces généralisations concernent des

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Tensor gauge fields in arbitrary representations of $GL(D,{\bf R})$: II. Quadratic actions

Xavier BEKAERT, Nicolas BOULANGER

Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible

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On matrix differential equations in the Hopf algebra of renormalization

Kurusch EBRAHIMI-FARD, Dominique MANCHON

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Bounds for the dimensions of $p$-adic multiple $L$-value spaces

Go YAMASHITA

First, we will define $p$-adic multiple $L$-values ($p$-adic MLV's), which are generalizations of Furusho's $p$-adic multiple zeta values ($p$-adic MZV's) in Section 2. Next, we prove bounds for the dimensions of $p$-adic MLV-spaces in Section 3, assumin

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Quantum effects in gravitational wave signals from cuspy superstrings

Diego CHIALVA, Thibault DAMOUR

We study the gravitational emission, in Superstring Theory, from fundamental strings exhibiting cusps. The classical computation of the gravitational radiation signal from cuspy strings features strong bursts in the special null directions associated to t

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Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

Maxim KONTSEVICH, Yan SOIBELMAN

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several questions, e.g. the notion of homological unit or A-inf

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$K(E_{10})$, Supergravity and Fermions

Thibault DAMOUR, Axel KLEINSCHMIDT, Hermann NICOLAI

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritte

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Coherent algebras and noncommutative projective lines

Dmitri PIONTKOVSKI

A well-known conjecture says that every one-relator discrete group is coherent. We state and partly prove an analogous statement for graded associative algebras. In particular, we show every that Gorenstein algebra $A$ of global dimension 2 is graded c

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About the Trimmed and the Poincaré-Dulac normal form of diffeomorphisms

Jacky CRESSON, Jasmin RAISSY

We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a self-contain introduction to the mould formalism of Jean

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Fractional embedding of differential operators and Lagrangian systems

Jacky CRESSON

This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordi

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Mode conversion in the cochlea? linear analysis

Robert S. MACKAY

It is suggested that the frequency selectivity of the ear may be based on the phenomenon of mode conversion rather than critical layer resonance. The distinction is explained and supporting evidence discussed.

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Stochastic Embedding of Dynamical Systems

Jacky CRESSON, Sébastien DARSES

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Théorème de Noether stochastique

Jacky CRESSON, Sébastien DARSES

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Non-differentiable deformations of $R^n$

Jacky CRESSON

Many problems of physics or biology involve very irregular objects like the rugged surface of a malignant cell nucleus or the structure of space-time at the atomic scale. We define and study non-differentiable deformations of the classical Cartesian spa

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Etude for linear Dyson-Schwinger Equations

Dirk KREIMER

We discuss properties of linear Dyson-Schwinger equations.

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An Etude in non-linear Dyson-Schwinger equations

Dirk KREIMER, Karen YEATS

We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized Green funct

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Curvature corrections and Kac-Moody compatibility conditions

Thibault DAMOUR, Amihay HANANY, Marc HENNEAUX, \ Axel KLEINSCHMIDT, Hermann NICOLAI

We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac--Moody algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005) 2849. We first emphasize thatt

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Evolution in random environment and structural instability

Sergey VAKULENKO, Dima GRIGORIEV

We consider stability and evolution of complex biological systems in particular, genetic networks. We focus our attention on supporting of homeostasis in these systems with respect to fluctuations of an external medium (the problem is posed by

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L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld au niveau des points

Laurent FARGUES

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Wilson Loops of Anti-symmetric Representation and D5-branes

Satoshi YAMAGUCHI

We use a D5-brane with electric flux in AdS_5 x S^5 background to calculate the circular Wilson loop of anti-symmetric representation in N=4 super Yang-Mills theory in 4 dimensions. The result agrees with the Gaussian matrix model calculation.

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Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators.

David RUELLE

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Matrix Representation of Renormalization in Perturbative Quantum Field Theory

Kurusch EBRAHIMI-FARD, Li GUO

We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota-Baxter anti-homomorphism from general regularized functionals on the Feynmang

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L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld : Décomposition cellulaire de la tour de Lubin-Tate

Laurent FARGUES

Cet article est le premier d'une série visant à construire un isomorphisme entre les tours p-adiques de Lubin-Tate et de Drinfeld, décrire cet isomorphisme et en donner des applications. Nous-y construisons un modèle entier p-adique équivariant en niveaui

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Birkhoff type decompositions and the Baker--Campbell--Hausdorff recursion

Kurusch EBRAHIMI-FARD, Li GUO, Dominique MANCHON

We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type decompositiont

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The structure of double groupoids

Nicolás ANDRUSKIEWITSCH, Sonia NATALE

We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our description goesa

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First steps towards p-adic Langlands functoriality

Christophe BREUIL, Peter SCHNEIDER

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modificati

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Existence of closed $G_2$-structures on 7-manifolds

Hong-Van LE

In this note we propose a new way of constructing compact 7-manifolds with a closed $G_2$-structure. As a result we find a first example of a closed $G_2$-structure on $S^3 imes S^4$. We also prove that any integral closed $G_2$-structure on a compact7-

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Existence d'immeubles triangulaires quasi-périodiques

Sylvain BARRÉ, Mikael PICHOT

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Ergodic pumping: a mechanism to drive biomolecular conformation changes

Robert S. MACKAY, David J.C. MACKAY

We propose that a significant contribution to the power stroke of myosin and similar conformation changes in other biomolecules is the pressure of a single molecule (e.g. a phosphate ion) expanding a trap, a mechanism we call ``ergodic pumping''. We demo

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Interaction of two charges in a uniform magnetic field I: planar problem

Diogo PINHEIRO, Robert S. MACKAY

The interaction of two charges moving in $R^2$ in a magnetic field ${f B}$ can be formulated as a hamiltonian system with 4 degrees of freedom. Assuming that the magnetic field is uniform and the interaction potential has rotational symmetry we reduceth

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Cerbelli and Giona's map is pseudo-Anosov and 9 consequences

Robert S. MACKAY

It is shown that a piecewise affine area-preserving homeomorphism of the 2-torus studied by Cerbelli and Giona is pseudo-Anosov. This enables one to prove various of their conjectures, quantify the multifractality of its "w-measures", calculate many ot

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Discommensuration Theory and Shadowing in Frenkel-Kontorova Models

Claude BAESENS, Robert S. MACKAY

We prove that if the minimum energy advancing discommensuration of mean spacing $p/q$ for a Frenkel-Kontorova chain is unique up to translations and has phonon gap then all minimum energy states with mean spacing $\omega$ just above $p/q$ are approximate

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Dirichlet forms and Markov semigroups on non-associative vector bundles

Cho-Ho CHU, Zhongmin QIAN

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Sur quelques représentations potentiellement cristallines de $GL_2(Q_p)$

Laurent BERGER, Christophe BREUIL

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Jordan structures in harmonic functions and Fourier algebras on homogeneous spaces

Cho-Ho CHU, Anthony To-Ming LAU

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Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Steven B. BRADLOW, Oscar GARCIA-PRADA, Peter B. GOTHEN

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On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces

Luis ALVAREZ-CONSUL, Oscar GARCIA-PRADA, Alexander H.W. SCHMITT

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Universal enveloping algebras and some applications in physics

Xavier BEKAERT

These notes are intended to provide a self-contained and pedagogical introduction to the universal enveloping algebras and some of their uses in mathematical physics. After reviewing their abstract definitions and properties, the focus is put on their

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Semi-global invariants of piecewise smooth Lagrangian fibrations

Ricardo CASTANO-BERNARD, Diego MATESSI

We study certain types of piecewise smooth Lagrangian fibrations of smooth symplectic manifolds, which we call stitched Lagrangian fibrations. We extend the classical theory of action-angle coordinates to these fibrations by encoding the information on th

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Hidden symmetries and the fermionic sector of eleven-dimensional supergravity

Thibault DAMOUR, Axel KLEINSCHMIDT, Hermann NICOLAI

We study the hidden symmetries of the fermionic sector of D=11 supergravity, and the role of K(E10) as a generalised `R symmetry'. We find a consistent model of a massless spinning particle on an E10/K(E10) coset manifold whose dynamics can be mapped ont

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On Killing tensors and cubic vertices in higher-spin gauge theories

Xavier BEKAERT, Nicolas BOULANGER, Sandrine CNOCKAERT, Serge LECLERCQ

The problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killi

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Relative Seiberg-Witten and Ozsvath-Szabo invariants for surfaces in 4-manifolds

Sergey FINASHIN

We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinem

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Collapsed 5-manifolds with pinched sectional curvature

Fuquan FANG, Xiaochun RONG

Let $M$ be a closed $5$-manifold of pinched curvature $0<\delta\le \text{sec}_M\le 1$. We prove that $M$ is homeomorphic to a spherical space form if $M$ satisfies one of the following conditions: (i) $\delta =1/4$ and the fundamental groupi

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A Chiral Perturbation Expansion for Gravity

Mohab ABOU ZEID, Christopher HULL

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Filtration de monodromie et cycles évanescents formels

Laurent FARGUES

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Refined Analytic Torsion as an Element of the Determinant Line

Maxim BRAVERMAN, Thomas KAPPELER

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the ref

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Lectures on curved beta-gamma systems, pure spinors, and anomalies

Nikita NEKRASOV

The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-linear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from thew

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On motives associated to graph polynomials

Spencer BLOCH, Hélène ESNAULT, Dirk KREIMER

The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the

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On obstructions to asphericity of certain crossed modules

Roman MIKHAILOV

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Noncritical osp($1 vert 2$,R) M-theory matrix model with an arbitrary time dependent cosmological constant

Jeong-Hyuck PARK

Dimensional reduction of the D=2 minimal super Yang-Mills to the D=1 matrix quantum mechanics is shown to double the number of dynamical supersymmetries, from N=1 to N=2. We analyze the most general supersymmetric deformation of the latter, in order to co

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Anatomy of a gauge theory

Dirk KREIMER

Resumé: We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson--Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free qua

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Théorie d'Iwasawa des représentations cristallines II

Denis BENOIS, Laurent BERGER

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Représentations modulaires de $mathrm{GL}_2(mathbf{Q}_p)$ et représentations galoisiennes de dimension $2$

Laurent BERGER

On montre la conjecture de Breuil concernant la r\'eduction modulo $p$ des repr\'esentations triangulines $V$ et des repr\'esentations $\Pi(V)$ de $\mathrm{GL}_2(\mathbf{Q}_p)$ qui leur sont associ\'ees par la correspondance de Langlands $p$-ad

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Kähler flat manifolds of low dimensions

Andrzej SZCZEPA'NSKI

We give a list of six dimensional flat K\"ahler manifolds. Moreover, we present an example of eight dimensional flat K\"ahler manifold M with finite Out(\pi_1(M)) group.

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The Hopf algebra structure of renormalizable Quantum Field Theory

Dirk KREIMER

Review for the Encyclopedia of Mathematical Physics.

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Quaternion Landau-Ginsburg models and noncommutative Frobenius manifolds

Sergey NATANZON

We extend topological Landau-Ginsburg models with boundaries to Quaternion Landau-Ginsburg models that satisfy the axioms for open-closed topological field theories. Later we prove that moduli spaces of Quaternion Landau-Ginsburg models are non-commuta

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The continuous spin limit of higher spin equations of motion

X. BEKAERT, J. MOURAD

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity

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On non-commutative analytic spaces over non-archimedean fields

Yan SOIBELMAN

We discuss various examples of non-commutative spaces which can be called non-commutative rigid analytic spaces

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On the torsion of optimal elliptic curves over function fields

Mihran PAPIKIAN

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Torsion as a function on the space of representations

Dan BURGHELEA, Stefan HALLER

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Dynamics, Laplace transform and Spectral geometry

Dan BURGHELEA, Stefan HALLER

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Jean Dieudonné (1906-1992) mathematician

Pierre CARTIER

Jean Dieudonn\'e has been one of the most influential French mathematicians during the 20$^{\rm th}$ century, especially through his association -- even identification -- with the Bourbaki group. An excellent biography has been written by his friend P.

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An algebraic proof of a cancellation theorem for surfaces

Anthony CRACHIOLA, Leonid MAKAR-LIMANOV

Let $\K$ be an algebraically closed field of arbitrary characteristic. We give a short self-contained algebraic proof of the following statement: If the cylinder over an affine surface (i. e. the product of our surface and an affine line) over $\K$ i

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Spin three gauge theory revisited

Xavier BEKAERT, Nicolas BOULANGER, Sandrine CNOCKAERT

We study the problem of consistent interactions for spin-$3$ gauge fields in flat spacetime of arbitrary dimension $n > 3$. Under the sole assumptions of Poincar\'e and parity invariance, local and perturbative deformation of the free theory, we det

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A group of diffeomorphisms of the interval with intermediate growth

Andrés NAVAS

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Sur la dynamique unidimensionnelle en régularité intermédiaire

Bertrand DEROIN, Victor KLEPTSYN, Andrés NAVAS

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Représentations p-adiques ordinaires de GL2(Qp) et compatibilité local-global

Christophe BREUIL, Matthew EMERTON

On définit les représentations p-adiques de GL2(Qp) "correspondant" aux représentations potentiellement cristallines réductibles (et éventuellement scindées) de Gal(Qpbar/Qp) de dimension 2 et on montre qu'elles apparaissent naturellement dans la coh

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Représentations semi-stables de $GL_2 ({mathbb Q}_p)$, demi-plan $p$-adique et réduction modulo $p$

Christophe BREUIL, Ariane MÉZARD

On calcule par voie cohomologique la r\'eduction modulo $p$ de certaines repr\'esentations $p$-adiques semi-stables de ${\rm GL}_2({\mathbb Q}_p)$. Les calculs exploitent la g\'eom\'etrie du demi-plan $p$-adique. Ils permettent de retrouver cert

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Cauchy-Davenport theorem in group extensions

Gyula KAROLYI

Let A and B be nonempty subsets of a finite group G in which the order of the smallest nontrivial subgroup is not smaller than d=|A|+|B|-1. Then the product set AB has at least d elements. This extends a classical theorem of Cauchy and Davenport to noncom

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Sur la conjecture faible de Greenberg dans le cas abélien $p$-décomposé

Thong NGUYEN QUANG DO

Let $p$ be an odd prime. For any CM number field $K$ containing a primitive $p^{\rm th}$-root of unity, class field theory and Kummer theory put together yield the well known reflection inequality $\lambda^+ \leq \lambda^-$ between the ``plus'' and`

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On the Riemann zeta-function and analytic characteristic functions

Anthony P. CSIZMAZIA

Set $f(s) :=1/(\sin(\pi s/4)q(1/2 + s))$ with $q(s) := \pi^{-s/2} \, 2 \Gamma (1 + s/2)(s-1) \zeta (s)$. The Riemann hypothesis, RH, and the simple zeros conjecture, SZC, together with conjectures advanced by the author are used to show that $f(s)$o

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Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology

Christoph BERGBAUER, Dirk KREIMER

In this review we discuss the relevance of the Hochschild cohomology of renormalization Hopf algebras for local quantum field theories and their equations of motion.

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Semi-stable extensions on arithmetic surfaces

Christophe SOULÉ

On a given arithmetic surface, inspired by work of Miyaoka, we consider vector bundles which are extensions of a line bundle by another one. We give sufficient conditions for their restriction to the generic fiber to be semi-stable. We then apply the

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Estimates from below for the spectral function and for the remainder in local Weyl's law

Dmitry JAKOBSON, Iosif POLTEROVICH

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proo

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Formal Lagrangian Operad

Alberto CATTANEO, Benoit DHERIN, Giovanni FELDER

Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication space is an ass

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Gauge invariants and Killing tensors in higher-spin gauge theories

Xavier BEKAERT, Nicolas BOULANGER

In free completely symmetric tensor gauge field theories on Minkowski space-time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.

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Partial wave expansion and Wightman positivity in conformal field theory

Nikolay M. NIKOLOV, Karl-Henning REHREN, Ivan T. TODOROV

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based on the assu

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Sur la réduction des représentations cristallines de dimension 2 en poids moyens

Laurent BERGER, Christophe BREUIL

On calcule la r\'eduction modulo $p$ des repr\'esentations cristallines de dimension $2$ dont les poids de Hodge-Tate sont $0$ et $k-1$ avec $k \in \{p+2,\cdots,2p-1\}$.

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On the Hochschild-Kostant-Rosenberg map for graded manifolds

Alberto CATTANEO, Domenico FIORENZA, Riccardo LONGONI

We show that the Hochschild--Kostant--Rosenberg map from the space of multivector fields on a graded manifold $N$ (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on $N$ (as a subalgebra of the Hochschi

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Rota-Baxter Algebras, Dendriform Algebras and Poincare-Birkhoff-Witt Theorem

Kurusch EBRAHIMI-FARD, Li GUO

Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double

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Dynamics of higher spin fields and tensorial space

I. BANDOS, X. BEKAERT, J.A. DE AZCARRAGA, D. SOROKIN, M. TSULAIA

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Biorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions

M. BERTOLA, M. GEKHTMAN

We consider the class of biorthogonal polynomials that are used to solve the inverse spectral problem associated to elementary co-adjoint orbits of the Borel group of upper triangular matrices; these orbits are the phase space of generalizedi

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On the Distribution of the Wave Function for Systems in Thermal Equilibrium

Sheldon GOLDSTEIN, Joel L. LEBOWITZ, Roderich TUMULKA, Nino ZANGHI

A density matrix that is not pure can arise, via averaging, from many different distributions of the wave function. This raises the question, which distribution of the wave function, if any, should be regarded as corresponding to systems in thermal eq

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An invariant for non simply connected manifolds

Dan BURGHELEA, Stefan HALLER

For a closed manifold $M$ we introduce the set of co-Euler structures and we define the modified Ray-Singer torsion, a positive real number associated to $M,$ a co-Euler structure and an acyclic representation $\rho$ of the fundamental group of $M$ wi

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Factorization Conjecture and the Open/Closed String Correspondence

Marcus BAUMGARTL, Ivo SACHS, Samson L. SHATASHVILI

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Analyticity of the susceptibility function for unimodal Markovian maps of the interval

Yunping JIANG, David RUELLE

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Gromov-Witten invariants and pseudo symplectic capacities

Guangcun LU

We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate iti

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A LA RECHERCHE DE LA m-THÉORIE PERDUE Z-THEORY: CHASING m/f THEORY

Nikita NEKRASOV

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LECTURES ON NONPERTURBATIVE ASPECTS OF SUPERSYMMETRIC GAUGE THEORIES

Nikita NEKRASOV

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GROMOV-WITTEN THEORY AND DONALDSON-THOMAS THEORY, II

D. MAULIK, N. NEKRASOV, A. OKOUNKOV, R. PANDHARIPANDE

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Global geometric deformations of current algebras as Krichever-Novikov type algebras

Alice FIALOWSKI, Martin SCHLICHENMAIER

We construct algebraic-geometric families of genus one (i.e. elliptic) current and affine Lie algebras of Krichever-Novikov type. These families deform the classical current, respectively affine Kac-Moody Lie algebras. The construction is induced by t

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Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence

Vassily GORBOUNOV, Fyodor MALIKOV

We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the Landau-Ginzburg orbifold. As an application, we prove an e

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On the Galois cohomology of unipotent algebraic groups over local and global function fields

Q.T. NGUYEN, D.T. NGUYEN

We discuss some results on the triviality and finiteness for Galois cohomology of connected unipotent groups over local and global function fields, and their relation with the closedness of orbits. As application, we show that a separable additive pol

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Nonlinear Higher Spin Theories in Various Dimensions

X. BEKAERT, S. CNOCKAERT, C. IAZEOLLA, M.A. VASILIEV

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Some Rationality Properties of Observable Groups and Related Questions

Thang NGUYEN QUOC, Bac DAO PHUONG

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Chiral polyhedra in ordinary space, II

Egon SCHULTE

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew faces and fini

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EXPLICIT MUMFORD ISOMORPHISM FOR HYPERELLIPTIC CURVES

Robin DE JONG

We give an explicit version of the Mumford isomorphism on the moduli stack of hyperelliptic curves of any given genus.

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LA MONODROMIE HAMILTONIENNE DES CYCLES ÉVANESCENTS

Mauricio GARAY

Nous montrons sous des hypoth\`eses pr\'ecis\'ees dans l'\'enonc\'e que le premier groupe d'homologie \'evanescente d'une fibration lagrangienne singuli\`ere est librement engendr\'e par les cycles \'evanescents. Nous en d\'eduison

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Four basic symmetry types in the universal 7-cluster structure of 143 complete bacterial genomic sequences

Alexander GORBAN, Tanya POPOVA, Andrei ZINOVYEV

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Fermions in the harmonic potential and string theory

A. BOYARSKY, V.V. CHEIANOV, O. RUCHAYSKIY

We explicitly derive collective field theory description for the system of fermions in the harmonic potential. This field theory appears to be a coupled system of free scalar and (modified) Liouville field. This theory should be considered as an exact bos

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Creation of Toy Universe

Eric NOVAK

General ideas of gauge/gravity duality allow for the possibility of time dependent solutions that interpolate between a perturbative gauge theory phase and a weakly curved string/gravity phase. Such a scenario applied to cosmology would exhibit a non-geom

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REPRÉSENTATIONS CRISTALLINES IRRÉDUCTIBLES DE ${

Laurent BERGER, Christophe BREUIL

Nous démontrons certaines conjectures (non nullit\'e, irr\'eductibilit\'e topologique, admissibilit\'e) dues au second auteur concernant des représentations unitaires de GL2(Qp) sur des espaces de Banach p-adiques associées aux représentations

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Boundary Liouville theory at $c=1$

Stefan FREDENHAGEN, Volker SCHOMERUS

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models

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On the Landau Background Gauge Fixing and the IR Properties of YM Green Functions

P.A. GRASSI, T. HURTH, A. QUADRI

We analyse the complete algebraic structure of the background field method for Yang--Mills theory in the Landau gauge and show several structural simplifications within this approach. In particular we present a new way to study the IR behavior of Green fu

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Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

Anton A. GERASIMOV, Samson L. SHATASHVILI

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important r

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THE K-THEORY OF HEEGAARD-TYPE QUANTUM 3-SPHERES

Paul BAUM, Piotr M. HAJAC, Rainer MATTHES, Wojciech Szyma'nski

We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal C*-algebras defining our quantum 3-spheres with a

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The Structure of the Ladder Insertion-Elimination Lie Algebra

Igor MENCATTINI, Dirk KREIMER

We continue our investigation into the insertion-elimination Lie algebra of Feynman graphs in the ladder case, emphasizing the structure of this Lie algebra relevant for future applications in the study of Dyson-Schwinger equations. We work

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Saddle point equations in Seiberg-Witten theory

Sergey SHADCHIN

N=2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU(N), SO(N), and Sp(N) is considered. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for (almost) al

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What is the trouble with Dyson--Schwinger equations?

Dirk KREIMER

We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the equation is lin

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Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

K. EBRAHIMI-FARD, L. GUO, D. KREIMER

In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recu

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Approximation by analytic operator functions. Factorizations and very badly approximable functions

V.V. PELLER, S.R. TREIL

This is a continuation of our earlier paper. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We discuss thematic and canonic

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AN EXTENSION OF THE KOPLIENKO-NEIDHARDT TRACE FORMULAE

Vladimir PELLER

Koplienko found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class $\bS_2$. A similar formula in the case of unitary operators was obtained by Neidhardt. In this paper we improve their results and obtain sh

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Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model

Alexander VARCHENKO

We show that the Shapovalov norm of a Bethe vector in the Gaudin model is equal to the Hessian of the logarithm of the corresponding master function at the corresponding isolated critical point. We show that different Bethe vectors are orthogonal. The

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Differentiating the absolutely continuous invariant measure of an interval map $f$ with respect to $f$

David RUELLE

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ABCD of instantons

Nikita NEKRASOV, Sergey SHADCHIN

We solve N=2 supersymmetric Yang-Mills theories for arbitrary classical gauge group, i.e. SU(N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We manage to do thisw

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Bernoulli Number Identities from Quantum Field Theory

Gerald V. DUNNE, Christian SCHUBERT

We present a new method for the derivation of convolution identities for finite sums of products of Bernoulli numbers. Our approach is motivated by the role of these identities in quantum field theory and string theory. We first show that the Miki id

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Holomorphically Covariant Matrix Models

Kazuyuki FURUUCHI

We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix coordinates.

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Distance Function, Linear quasi-Connections and Chern Character.

Nicolae TELEMAN

In Sect.4 we show how the Chern character of the tangent bundle of a smooth manifold may be extracted from the geodesic distance function by means of cyclic homology. In Sect.5 we introduce the notion of coarse linear connection in vector bundles, noti

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Optimal Trade-Off for Merkle Tree Traversals

P. BERMAN, M. KARPINSKI, Y. NEKRICH

We prove tight upper and lower bounds for computing Merkle tree traversals, and display optimal trade-offs between time and space complexity of that problem.

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Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order

Luc BLANCHET, Thibault DAMOUR, Gilles ESPOSITO-FARÈSE, Bala R. IYER

The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN sou

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Mathematical models in population dynamics and ecology

Rui DILÃO

We introduce the most common quantitative approaches to population dynamics and ecology, emphasizing the different theoretical foundations and assumptions. These populations can be aggregates of cells, simple unicellular organisms, plants or animals.

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Approximation Hardness of Short Symmetric Instances of MAX-3SAT

P. BERMAN, M. KARPINSKI, A. SCOTT

We prove approximation hardness of short symmetric instances of MAX-3SAT in which each literal occurs exactly twice, and each clause is exactly of size 3. We display also an explicit approximation lower bound for that problem. The bound two on the numbe

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Deformation of outer representations of Galois group

Arash RASTEGAR

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, weintro

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Phasing of gravitational waves from inspiralling eccentric binaries

T. DAMOUR, A. GOPAKUMAR, B.R. IYER

We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals

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Conformal invariance and rationality in an even dimensional quantum field theory

N.M. NIKOLOV, I.T. TODOROV

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Vertex Operators for Closed Superstrings

P.A. GRASSI, L. TAMASSIA

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic backgroun

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Self-similar Fractals in Arithmetic

Arash RASTEGAR

We define a notion of self-similarity on algebraic varieties by considering algebraic endomorphisms as "similarity" maps. Self-similar objects are called fractals, for which we present several examples and define a notion of dimension in many differentc

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The residues of quantum field theory - numbers we should know

Dirk KREIMER

We discuss in an introductory manner structural similarities between the polylogarithm and Green functions in quantum field theory.

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Noncentral extension of the $AdS_{5} \times S^{5}$ superalgebra : supermultiplet of brane charges

Sangmin LEE, Jeong-Hyuck PARK

We propose an extension of the su(2, 2|4) superalgebra to incorporate the F1/D1 string charges in type IIB string theory on the $AdS_{5} \times S^{5}$ background, or the electro-magnetic charges in the dual super Yang-Mills theory. With the charges intro

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D-brane charges on SO(3)

Stefan FREDENHAGEN

In this letter we discuss charges of D-branes on the group manifold SO(3). Our discussion will be based on a conformal field theory analysis of boundary states in a Z_2-orbifold of SU(2). This orbifold differs from the one recently discussed by Gaberdiela

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Weak Bézout inequality for D-modules

Dima GRIGORIEV

A bound is obtained on the leading coefficient of the Hilbert-Kolchin polynomial of a D-module in terms of the degrees of its generators.

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The Hopf algebra of rooted trees in Epstein-Glaser Renormalization

Christoph BERGBAUER, Dirk KREIMER

We show how the Hopf algebra of rooted trees, in a somewhat modified presentation, encodes the combinatorics of Epstein-Glaser renormalization and position space renormalization in general. In particular we prove that the Epstein-Glaser time-ordered produ

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S-duality and Topological Strings

Nikita NEKRASOV, Hirosi OOGURI, Cumrun VAFA

In this paper we show how S-duality of type IIB superstrings leads to an S-duality relating A and B model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitude

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Lusternik-Schnirelman theory and dynamics, II

M. FARBER, T. KAPPELER

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An introduction to arithmetic groups

Christophe SOULÉ

Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by generators and re

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Integrable Renormalization II: the general case

Kurusch EBRAHIMI-FARD, Li GUO, Dirk KREIMER

We extend the results we obtained in an earlier. The cocommutative case of rooted ladder graphs is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decompositio

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Torsion cohomology classes and algebraic cycles on complex projective manifolds

C. SOULÉ, C. VOISIN

Atiyah and Hirzebruch gave examples of even degree torsion classes in the singular cohomology of a smooth complex projective manifold, which are not Poincaré dual to an algebraic cycle. We notice that the order of these classes are small compared to the d

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Systèmes de Taylor-Wiles pour ${\rm GSp}_4$

Alain GENESTIER, Jacques TILOUINE

On montre qu'une représentation galoisienne symplectique de degré quatre congrue modulo p à une représentation galoisienne provenant d'une forme de Siegel de genre deux provient elle-même d'une telle forme de Siegel. On suppose pour cela que l'image d

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Classical/quantum integrability in AdS/CFT

V.A. KAZAKOV, A. MARSHAKOV, J.A. MINAHAN, K. ZAREMBO

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An inverse theorem for the restricted set addition in Abelian groups

Gyula KÁROLYI

Let $A$ be a set of $k\ge 5$ elements of an Abelian group $G$ in which the order of the smallest nontrivial subgroup is larger than $2k-3$. Extending a result of Dias da Silva and Hamidoune (Bull. London Math. Soc. 26 (1994) 140-146), in a recent paperwe

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Spectral Asymmetry, Zeta Functions and the Noncommutative Residue

Raphaël PONGE

In this paper, motivated by an approach developped by Wodzicki, we look at the spectral asymmetry of elliptic PsiDO's in terms of theirs zeta functions. First, using asymmetry formulas of Wodzicki we study the spectral asymmetry of odd elliptic PsiDO'sa

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The entropy of black holes: a primer

Thibault DAMOUR

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiat

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Cayley-Hamilton Decomposition and Spectral Asymmetry

Raphaël PONGE

In this paper we derive Cayley-Hamilton decompositions, along some of their consequences, for compact operators and closed operators with compact resolvent on a (separable) Hilbert space. In particular, we make use these decompositions to give a spectrali

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Unraveling the Fourier Law for Hamiltonian Systems

Jean-Pierre ECKMANN, Lai-Sang YOUNG

We exhibit simple Hamiltonian and stochastic models of heat transport in non-equilibrium problems. Theoretical arguments are given to show that, for a wide class of models, the temperature profile obeys a universal law depending on a parameter $\alpha $.