Lieu: IHP, amphi Hermite.
The seminar will take place in presence, but will be broadcasted via the zoom link:
https://us02web.zoom.us/j/81272974677?pwd=cEtMRHJJcldqUSs2Tlp4dE9lbHpiZz09
10:45 Klaus Niederkrüger (Lyon)
An overtwisted convex hypersurface in dim>3.
Abstract:. The
generalization of the notion of "overtwisted contact structures" to
dim>3 by Borman-Eliashberg-Murphy (BEM) has been of huge impact for
high dimensional contact topology. Their definition is extremely
technical though, and it is only due to Casals-Murphy-Presas that we
dispose of necessary tools to recognize some real-life examples of
overtwisted (in the sense of BEM) contact manifolds.
Nonetheless, we
feel that among the equivalent definitions found so far, there is none
that is as basic as the 3-dimensional overtwisted disk.
In my talk, I
will explain why a certain convex hypersurface is overtwisted, and what
would still be needed to be understood to claim that this hypersurface
is "the overtwisted disk" in higher dimension
14:00 Thibaut Mazuir (Jussieu)
Higher algebra of A-infinity algebras in Morse theory
Abstract: In this talk, I will introduce the notion of n-morphisms between two
A-infinity algebras. These higher morphisms are such that 0-morphisms
correspond to standard A-infinity morphisms and 1-morphisms correspond
to A-infinity homotopies. The set of higher morphisms between two
A-infinity-algebras then defines a simplicial set which has the
property of being a Kan complex. The combinatorics of
n-morphisms are moreover encoded by new families of polytopes, which I
call the n-multiplihedra and which generalize the standard
multiplihedra.
Elaborating on works by Abouzaid and Mescher, I will then explain how
this higher algebra of A-infinity algebras naturally arises in the
context of Morse theory.
15:45 Claude Viterbo (Orsay) - To be confirmed
Stochastic Homogenization for Hamilton-Jacobi equations
Abstract: To a Hamiltonian microscopically periodic on $\mathbb R^{2n}$, we can associate a macroscopic Hamitlonian depending only on the variable $p$. This result is due to Lions-Papanicolaou-Varadhan for viscosity solutions and to the author for variational solutions. We
shall deal here for variational solutions with the case of a random
Hamiltonian and the conclusion is similar : we see macroscopically an
effective Hamiltonian $\overline H (p)$. In the viscosity case, this
is only known for $H$ convex in $p$ (Rezakhanlou-Tarver and
Souganidis). The proof involves besides symplectic
topological methods, some approximation methods for non-smooth
Hamiltonians and some old results on the structure of compact abelian
groups.
Prochaines séances: 12 novembre, 3 décembre.
Autre activité symplectique à Paris:
- Exposé de Vivek Shende au séminaire d'analyse algébrique de Jussieu le 18 octobre à 14h.
- Séminaire Nantes-Orsay
