**Responsable d’équipe :** François Loeser**Responsables adjoints :** Penka GEORGIEVA, Maxime ZAVIDOVIQUE**Gestionnaire :** Julienne PASSAVE

Adresse postale :

IMJ-PRG – UMR7586 Université Pierre et Marie Curie Boite courrier 247 Couloir 15-25 5e étage 4 place Jussieu, 75252 Paris Cedex 05 |

L’après-midi de l’équipe aura lieu** le 12/11/2024 **en salle** 15.16.413.**

**Programme :**

15h00 – 17h30 : Exposés des nouveaux arrivants de l’équipe (titres et résumés plus bas)

15h00 – 15h40 : Russell Avdek

15h50 – 16h30 : Felipe Espreafico Guelerman Ramos

16h40 – 17h20 : Ioannis Iakovoglou

17h30 – 18h : Réunion de l’équipe

**À partir de 18h00 : pot dans la salle 15.16.417**

**Résumés des exposés :**

Russell Avdek

Title : Algebraic invariants of contact manifolds

Abstract : Contact manifolds appear naturally in complex geometry and smooth topology, and the talk will start with some famous examples. Afterwards, I’ll review some algebraic invariants of contact manifolds and discuss how they relate to known algebraic structures like loop space homologies and quantum knot invariants. Time permitting, I’ll summarize some of my related ongoing projects.

Felipe Espreafico Guelerman Ramos

Title : Counting Lines on Hypersurfaces: beyond real and complex counts

Abstract : Since our mathematical infancy, we learn that a complex cubic surfaces on the projective space have 27 lines. After that, we quickly learn how to get similar numbers for higher dimensional hypersurfaces. Using the machinery from $A^1$-homotopy theory, it is possible to compute counts for lines over a general field $k$ which are not integers, but quadratic forms. In these counts, each line contributes with a local index, which is given by a quadratic form. In this talk, we explain how to obtain such counts and explore the geometric nature of the local contributions. This is joint with Sabrina Pauli and Stephen McKean.

Ioannis Iakovoglou

Title : Classifying Anosov flows in dimension 3 by geometric types

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.