Institut de recherche mathématique avancée

Résumé : I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations. The proof is based on the construction of contact capacities coming from spectral selectors defined on the contactomorphisms group of the latter contact manifolds. I will define all these notions during my talk.

Résumé : In this talk, we present results on the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2$ blown up once under the presence of a Hamiltonian circle and finite cyclic group actions. We show how questions about the homotopy type are related to questions about extensions of group actions. Time permitting, we shall also discuss upcoming work on homotopy type of equivariant embedding spaces and their relation to symplectomorphism groups.

Résumé : Résumé : Un arbre couvrant d'un graphe connexe fini G est un sous-graphe connexe de G qui contient chaque sommet et ne contient aucun cycle. Un résultat bien connu d'Aldous énonce que la limite d'échelle de l'arbre couvrant uniforme du graphe complet est l'arbre brownien. En fait cet énoncé est plus général : l'arbre brownien est la limite d'échelle des arbres couvrants uniformes pour un grand ensemble de graphes en grande dimension. Dans cet exposé, nous allons essayer d'expliquer ce phénomène universel. Si le temps nous permet, nous allons également discuter des limites d’échelle des arbres couvrants aléatoires non-uniformes. Travaux en collaboration avec Asaf Nachmias et Matan Shalev.

Résumé : I will talk about the hydrostatic approximation of the Euler-Boussinesq equations, describing the evolution of an inviscid stratified fluid where the vertical length scale is much smaller than the horizontal one. Even though of importance in oceanography, the justification of the hydrostatic limit in this context has remained an open problem. I will discuss some recent results showing that some instability mechanisms may prevent this limit to hold. This is joint work with R. Bianchini (CNR Rome) and M. Coti Zelati (Imperial College London).

Résumé : The notion of 2-Segal space was defined by Dyckerhoff and Kapranov, and independently under the name of decomposition space by Gálvez-Carrillo, Kock, and Tonks. These structures encode algebraic objects for which composition need not always exist or be unique, yet still satisfy associativity. There are many examples of 2-Segal spaces, but two main applications stand out. First, 2-Segal spaces arise from the Waldhausen S-construction in algebraic K-theory. Second, they give rise to Hall algebra constructions, of interest in representation theory. In this talk, we'll look at a specific family of discrete 2-Segal spaces, or 2-Segal sets, associated to finite graphs, and how we can understand these two very general constructions in this setting. In particular, we'll show that many of the associated Hall algebras can be identified with cohomology algebras of familiar topological spaces.