Séminaires : Séminaire de Topologie

Equipe(s) : tga,
Responsables :Catherine Gille et Najib Idrissi
Email des responsables :
Salle : 1016
Adresse :Sophie Germain

Un plan d’accès est disponible ici. Pour vous inscrire à la liste de diffusion du séminaire, veuillez vous rendre à cette adresse.

Le séminaire de topologie évolue. Des après-midi de topologie seront organisées tout au long de l'année (en collaboration avec USPN) et nous vous en tiendrons informé(e)s sur cette liste de diffusion.

Orateur(s) Ismaïl Razack - , Anna Sopena Gilboy - , Lukas Waas - ,
Titre Après-midi de topologie : cinquième édition
Horaire14:00 à 18:00

Après-midi de Topologie - jeudi 7 mars 2024

Organisée par Christian Ausoni (LAGA), Geoffroy Horel (LAGA), Muriel Livernet (IMJ-PRG), Najib Idrissi (IMJ-PRG).

Ismaïl Razack: Hochschild cohomology, Batalin-Vilkovisky algebras and operads

The Hochschild cohomology of a differential graded algebra (DGA) is naturally endowed with a Gerstenhaber algebra structure. This structure can be enhanced into a Batalin-Vilkovisky algebra (BV algebra) when the DGA verifies some form of symmetry. For instance,  Luc Menichi showed that HH*(C*(M)), the Hochschild cohomology of the cochain complex of a smooth, compact, simply connected manifold M, is  a BV-algebra. The goal of this talk is to give a new proof of this  result using operad theory (Barratt-Eccles operad) and without  assuming that M is simply connected. We'll also explain why we get a  similar result if we replace a manifold by a pseudomanifold.

Ana Sopena Gilboy: Pluripotential operadic calculus

For complex manifolds, there exists a refined notion of weak equivalence related to both Dolbeault and anti-Dolbeault cohomology. This class of weak equivalences naturally defines a stronger formality notion. In particular, satisfying the ddbar-Lemma property does not imply formality in this new sense. The goal of this talk is to introduce a novel operadic framework designed to understand this homotopical situation. I will present pluripotential A-infinity algebras as well as a homotopy transfer theorem based on this strong notion of weak equivalence.

Lukas Waas: The topological stratified homotopy hypothesis

Roughly speaking, the homotopy hypothesis - due to Grothendieck - states that the homotopy theory of spaces should be the same as the homotopy  theory of infinity-groupoids. Ayala, Francis and Rosenblyum conjectured a stratified topological analogue of this principle: The homotopy theory of (topological) stratified spaces should be the same as the homotopy theory of layered infinity-categories, i.e. such infinity-categories in which every endomorphism is an isomorphism. We are going to present a formal interpretation of this statement. Namely, we prove the existence of a simplicial semi-model structure for stratified spaces in which most geometrically relevant examples – such as Whitney stratified spaces and PL pseudomanifolds - are bifibrant. We then prove a Quillen equivalence (in terms of Lurie’s exit-path construction) of this model category with a left Bousfield localization of the Joyal model structure presenting layered infinity-categories. In particular, the following interpretation of the topological homotopy hypothesis follows: Lurie’s exit-path construction induces an equivalence between the localization of bifibrant stratified spaces at stratified homotopy equivalences and the homotopy theory of layered infinity-categories.

AdresseUniversité Sorbonne Paris Nord