l’après-midi de l’équipe aura lieu le 05/03/2024 en salle 15.16.413.
Programme :
14h30 - 16h50 : Exposés des nouveaux arrivants dans l’équipe (titres et résumés plus bas)
14h30 - 15h10 Erman Cineli
15h20 - 16h00 Tudor Padurariu
16h10 - 16h50 Amanda Hirschi
16h50 - 17h15 : Réunion de l’équipe
À partir de 17h30 : pot dans la salle 15.16.417
Résumés des exposés :
Erman Cineli
Title: Invariant Sets and Hyperbolic Periodic Orbits of Reeb Flows
Abstract: In this talk we will discuss the impact of hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbits on the global dynamics of Reeb flows on the standard contact sphere. We will discuss extensions of two results previously known for Hamiltonian diffeomorphisms to the Reeb setting. The first one asserts that, under a very mild dynamical convexity type assumption, the presence of one hyperbolic closed orbit implies the existence of infinitely many simple closed Reeb orbits. The second result is a higher-dimensional Reeb analogue of the Le Calvez-Yoccoz theorem, asserting that no closed orbit of a non-degenerate dynamically convex Reeb pseudo-rotation is isolated as an invariant set. The talk is based on a joint work with Viktor Ginzburg, Basak Gurel and Marco Mazzucchelli.
Tudor Padurariu
Title: Quasi-BPS categories for K3 surfaces
Abstract: BPS invariants and cohomology are central objects in the study of (Kontsevich-Soibelman) Hall algebras or in enumerative geometry of Calabi-Yau 3-folds.
In joint work with Yukinobu Toda, we introduce a categorical version of BPS cohomology for local K3 surfaces, called quasi-BPS categories. When the weight and the Mukai vector are coprime, the quasi-BPS category is smooth, proper, and with trivial Serre functor etale locally on the good moduli space. Thus quasi-BPS categories provide (twisted) categorical (etale locally) crepant resolutions of the moduli space of semistable sheaves on a K3 surface for generic stability condition and a general Mukai vector. Time permitting, I will also discuss a categorical version of the \chi-independence phenomenon for BPS invariants.
Amanda Hirschi
Title : Going global
Abstract : Moduli spaces of pseudoholomorphic curves , while providing powerful symplectic invariants, are generally difficult to work with due to transversality problems. In 2021, Abouzaid-McLean-Smith achieved a breakthrough by constructing a nice representation, called a global Kuranishi chart, for the moduli space of stable maps to a symplectic manifold. While briefly sketching the construction, I will mainly focus on explaining some applications to pseudoholomorphic curve theory.