Density of potentially crystalline representations of fixed weight
Eugen HELLMANN, Benjamin SCHRAEN - 2013-11-15 (M/13/37)
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 deformation ring R. If we fix a regular set of Hodge-Tate weights k, we prove, under some hypothesis, that the closed points of Spec(R[1/p]) corresponding to potentially crystalline representations of fixed Hodge-Tate weights k are dense in Spec(R[1/p]) for the Zariski topology. The main hypothesis we need is the existence of a potentially diagonalizable lift, so that in the two-dimensional case, the result is unconditional.
Eigenvalues of Laplacian and multi-way isoperimetric constants on weighted Riemannian manifolds
Kei FUNANO - 2013-10-21 (M/13/36)
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 geometric quantity, called multi-way isoperimetric constants, on such manifolds and obtain similar universal inequalities among them. Multi-way isoperimetric constants are generalizations of the Cheeger constant. Extending and following the heat semigroup argument by Ledoux and E. Milman, we extend the Buser-Ledoux result to the k-th eigenvalue and the -way isoperimetric constant. As a consequence the k-th eigenvalue of the weighted Laplacian and the k-way isoperimetric constant are equivalent up to polynomials of k on closed weighted manifolds of nonnegative Bakry-
Allure of Quotations and Enchantment of Ideas
Misha GROMOV - 2013-10-02 (M/13/35)

Ergostructures, Ergologic and the Universal Learning Problem: Chapters 1, 2, 3
Misha GROMOV - 2013-10-01 (M/13/34)

Poisson varieties from Riemann surfaces
Philip BOALCH - 2013-09-30 (M/13/33)

The elliptic dilogarithm for the sunset graph
Spencer BLOCH, Pierre VANHOVE - 2013-09-24 (P/13/24)

The geometry of variations in Batalin-Vilkovisky formalism
Arthemy KISELEV - 2013-09-15 (M/13/32)
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. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's delta-function as a limit of smooth kernels. We illustrate the reasoning by re-deriving -but not just "formally postulating"- the standard properties of BV-Laplacian and Schouten bracket and by verifying their basic inter-relations (e.g., cohomology preservation by gauge symmetries of the quantum master-equation).
On-shell Techniques and Universal Results in Quantum Gravity
N.E.J. BJERRUM-BOHR, John F. DONOGHUE, Pierre VANHOVE - 2013-09-04 (P/13/23)

Quantum supersymmetric cosmology and its hidden Kac--Moody structure
Thibault DAMOUR, Philippe SPINDEL - 2013-09-04 (P/13/29)

Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
Donato BINI, Thibault DAMOUR - 2013-09-04 (P/13/30)

Merger states and final states of black hole coalescences: a numerical-relativity-assisted effective-one-body approach
Thibault DAMOUR, Alessandro NAGAR, Loic VILLAIN - 2013-09-04 (P/13/31)

The tensor hierarchy algebra
Jakob PALMKVIST - 2013-09-02 (P/13/27)

The tensor hierarchy simplified
Jesper GREITZ, Paul HOWE, Jakob PALMKVIST - 2013-09-02 (P/13/28)

The Nielsen and the Reidemeister Zeta Functions of maps on infra-solvmanifolds of type (R)
Alexander FELSHTYN, Jong Bum LEE - 2013-08-30 (M/13/26)
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 Nielsen zeta functions and the Reidemeister torsions of the corresponding mapping tori. We show that if the Reidemeister zeta function is defined for a homeomorphism on an infra-solvmanifold of type (R), then this manifold is an infra-nilmanifold. We also prove that a map on an infra-solvmanifold of type (R) induced by an affine map minimizes the topological entropy in its homotopy class and it has a rational Artin-Mazur zeta function. Our main technical tool is the averaging formulas for the Lefschetz, the Nielsen and the Reidemeister numbers on infra-solvmanifolds of type (R).
Anyon wave functions and probability distributions
Douglas LUNDHOLM - 2013-08-06 (P/13/25)
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 distributions encoded in the wave functions. Furthermore, a class of states which has been proposed in the context of upper bounds for a related many-anyon problem, is here considered from the point of view of these refined lower bounds. A numerical approach to determining their corresponding probability distributions is employed for a limited number of particles.
Ramification and nearby cycles for l-adic sheaves on relative curves
Haoyu HU - 2013-07-09 (M/13/22)
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 theory.
Conformal and Einstein gravity in twistor space
Tim ADAMO, Lionel MASON - 2013-06-18 (P/13/13)

Distributional Geometry of Squashed Cones
Dmitri FURSAEV, Alexander PATRUSHEV, Sergey SOLODUKHIN - 2013-06-17 (P/13/21)
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 rotational $O(2)$ symmetry in a subspace orthogonal to a singular surface $\Sigma$ so that the surface is allowed to have extrinsic curvatures. A new feature of squashed conical singularities is that the surface terms in the integral invariants, in the limit of small angle deficit, now depend also on the extrinsic curvatures of $\Sigma$. A case of invariants which are quadratic polynomials of the Riemann curvature is elaborated in different dimensions and applied to several problems related to entanglement entropy. The results are in complete agreement with computations of the logarithmic terms in entanglement entropy of 4D conformal theories \cite{Solodukhin:2008dh}. Among other applications of the suggested method are logarithmic terms in entanglement entropy of non-conformal theories and a holographic formula of entanglement entropy for theories with gravity duals.
Nonholonomic deformation of coupled and supersymmetric KdV equation and Euler-Poincaré-Suslov method
Partha GUHA - 2013-06-14 (M/13/15)
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 infinite-dimensional analogue of the Euler-Poincarnsional construction to construct nonholonomic deformation of a wide class of coupled KdV equations, all these equations follow from the Euler-PoincarS^1) \bo C^{\infty}(S^1)}}$, where$Diff(S^1)$is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to two component Camassa-Holm equation. We also give a derivation of a nonholonomic deformation of the$N=1$supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler-Poincar 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 - 2013-06-14 (M/13/16) 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 explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in the activator and inhibitor model and these are connected to conformal Hamiltonian structure. The role of the Jacobi Last Multiplier in Nonholonomic Systems and Almost Symplectic Structure Partha GUHA - 2013-06-14 (M/13/17) 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 structure associated to nonholonomic system, studied by L. Bates and his coworkers, can be mapped to symplectic form and canonical Poisson structure using JLM. We demonstrate how JLM can be used to map an integrable nonholonomic system to a Liouville integrable system. We map the toral fibration defined by the common level sets of the integrals of a Liouville integrable Hamiltonian system with a toral fibration coming from a completely integrable nonholonomic system. Contiguity relations for linearisable systems of Gambier type Alfred RAMANI, Basil GRAMMATICOS, Partha GUHA - 2013-06-14 (P/13/18) 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 Schlesinger transformations and the contiguity relations of the solutions of the Gambier mapping. In all cases the resulting contiguity relation is a linearisable equation, involving free functions, and which can be related to the generic Gambier mapping. Quantum aspects of the Liénard II equation and Jacobi's Last Multiplier-II Anindya GHOSE CHOUDHURY, Partha GUHA - 2013-06-14 (P/13/19) 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 to bound-state solutions of the Schr Chemotherapy in heterogeneous cultures of cancer cells with interconversion Rui DILãO - 2013-06-14 (M/13/20) 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 cancer stem cells, showing that, targeting only cancer stem cells with cytotoxic agents, it is not always possible to eradicate cancer. We have determined the kinetic conditions under which cytotoxic agents in \textit{in vitro} heterogeneous cultures of cancer cells eradicate cancer. In particular, we have shown that the chemotherapeutic elimination of \textit{in vitro} cultures of heterogeneous cancer cells is effective if it targets all the cancer cell types, and if the induced death rates for the different subpopulations of cancer cell types are large enough. Nouveaux développements sur les valeurs des caractères des groupes symétriques; méthodes combinatoires Pierre CARTIER - 2013-06-05 (M/13/14) 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 récemment , elles ont été appliquées par Biane aux propriétés asymptotiques des permutations. Nous insisterons surtout sur les formules exactes qui sous-tendent ces formules asymptotiques obtenues par les collaborateurs de Biane (Sniady, Féray), et qui développent de nouveaux domaines de la combinatoire (principalement cartes planaires). Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function Hafedh HERICHI, Michel L. LAPIDUS - 2013-05-15 (M/13/12) mRNA diffusion as a mechanism of morphogenesis in Drosophila early development Rui DILãO - 2013-04-29 (M/13/11) 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 ovary cells and is transported into the oocyte along microtubules. Initially, the oocyte has only one nucleus, but after fertilization and deposition of the egg, nuclear duplication by mitosis is initiated without the formation of cellular membranes. During the first 14 nuclear divisions of the developing embryo, bicoid mRNA of maternal origin is translated into protein in the ribosomes and accumulates near the external nuclear walls of the recently formed nuclei. Here, we show that mRNA diffusion is the main morphogenesis mechanism explaining consistently the establishment of Bicoid protein gradients. Moreover, we show that if diffusion for both bicoid mRNA and Bicoid protein were assumed, a steady distribution of Bicoid protein would result, with a constant concentration along the embryo, contradicting observations. Equivariant operational Chow rings of spherical varieties and T-linear varieties. Richard Paul GONZALES VILCARROMERO - 2013-04-12 (M/13/10) 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 varieties admitting a BB-decomposition into algebraic rational cells. Our description extends certain topological results to intersection theory on singular varieties. Dynamic trajectory control of gliders Rui DILãO, João FONSECA - 2013-04-04 (M/13/09) 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-powered lift-enabled vehicle (glider) travelling in planetary atmospheres. As a proof of concept, we have applied the new algorithm to the command and control of the trajectory of the Space Shuttle during the Terminal Area Energy Management (TAEM) phase. Chemotaxis with directional sensing during Dictyostelium aggregation Rui DILãO, Marcus HAUSER - 2013-03-24 (M/13/07) 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 chemotactic waves and on the gradient of the concentration of the chemoattractant. It is shown that the directional sensing of amoebae is due to the sensitivity of the cells to the time variation of the concentration of the chemoattractant combined with its gradient. It is also shown that chemotaxis exclusively driven by local concentration gradients leads to unstable local motion, preventing cells from aggregation. These facts show that the formation of mounds, which initiate multicellularity in Dictyostelium discoideum, is caused by the sensitivity of the amoebae to three factors, namely, to the direction of propagation of the chemoattractant, to its gradient, and to the spiral spatial topology of the propagating chemoattractant. The regulation of gene expression in eukaryotes: bistability and oscillations in repressilator models Rui DILãO - 2013-03-24 (M/13/08) 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 nucleoplasm and the protein synthesis in the cytoplasm. After re-parameterisation of the m-repressilator model with the Hill cooperative parameter n, for n=1, the m-repressilator is deductible from the mass action law and, in the limit$n \to \infty\$, it is a Boolean type model. With this embedding and with delays, if m is odd and n>1, we show that there is always a choice of parameters for which the m-repressilator model has sustained oscillations (limit cycles), implying that the 1-repressilator is the simplest genetic mechanism leading to sustained oscillations in eukaryotes. If m is even and n>1, there is always a choice of parameters for which the m-repressilator model has bistability.
Noyaux du transfert automorphe de Langlands et formules de Poisson non linéaires: Notes de cours
Laurent LAFFORGUE - 2013-02-18 (M/13/06)

On weakly group-theoretical non-degenerate braided fusion categories
Sonia NATALE - 2013-02-01 (M/13/05)
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 solvable non-degenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.
Special Functions in Minimal Representations
Toshiyuki KOBAYASHI - 2013-01-22 (M/13/04)
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.
Rankin-Cohen Operators for Symmetric Pairs
Toshiyuki KOBAYASHI, Michael PEVZNER - 2013-01-10 (M/13/03)

Sur la correspondance de Simpson p-adique. II : aspects globaux
Ahmed ABBES, Michel GROS - 2013-01-09 (M/13/02)
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 aspects of the theory.
Sur la correspondance de Simpson p-adique. 0 : une vue d'ensemble
Ahmed ABBES, Michel GROS - 2013-01-09 (M/13/01)
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 extensive overview of the theory that has been developped in two articles, the first one (arXiv:1102.5466) devoted to the local aspects and the second one (arXiv:1301.0904) to the global aspects.