Some aspects of topological Galois theory
Olivia CARAMELLO, Laurent LAFFORGUE - 2018-09-04 (M/18/09)
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 description of the atomic completion of a small category whose opposite satisfies the amalgamation pro- perty, and we explore to which extent a model of a Galois-type theory is determined by its symmetries.
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 - 2018-06-18 (M/18/08)
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 renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common framework.
On the Ramanujan conjecture for automorphic forms over function fields I. Geometry
Will SAWIN, Nicolas TEMPLIER - 2018-05-31 (M/18/07)

Global bifurcations of limit cycles in the Leslie-Gover model with the Allee effect
Valery A. GAIKO, Jean-Marc GINOUX, Cornelis VUIK - 2018-05-23 (M/18/06)
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 bifurcations, we prove that such a system can have at most two limit cycles surrounding one singular point. We also conduct some numerical experiments to illustrate the obtained results.
Multi-parameter planar polynomial dynamical systems
Valery GAIKO, Cornelis VUIK - 2018-04-13 (M/18/05)
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 effects of all their field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the Wintner-Perko termination principle and application of canonical systems with field rotation parameters. Using this method, we solve, e.g., Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the general Li\'{e}nard polynomial system and a Holling-type quartic dynamical system. We also conduct some numerical experiments to illustrate the obtained results.
Pre-Calabi-Yau algebras as noncommutative Poisson structures
Natalia IYUDU, Maxim KONTSEVICH - 2018-03-27 (M/18/04)
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 $Ac part of this solution is described, which is in one-to-one correspondence with the double Poisson algebra structure. As a consequence we have that appropriate pre-Calabi-Yau structures induce a Poisson bracket on representation spaces$({\rm Rep}_n A)^{Gl_n}$for any associative algebra$A$. Introduction to Higher Cubical Operads. Second Part: The Functor of Fundamental Cubical Weak$\infty\$-Groupoids for Spaces
Camell KACHOUR - 2018-01-16 (M/18/03)

Some Aspects of Dynamical Topology: Dynamical Compactness and Slovak Spaces