Lieu: IHP, salle 201

The seminar will take place in presence, but will be broadcasted via** **zoom

https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

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**10:45** Basak Gurel (Florida)

Forced existence of periodic orbits in symplectic dynamics.*Abstract: *In this talk, we will consider the phenomenon of “forced” existence of infinitely many periodic orbits from a broad perspective and discuss several results and open questions in a variety of settings. In particular, we will touch upon and sketch a relatively simple proof of a recent result of Egor Shelukhin, extending a celebrated theorem of Franks to higher dimensions. The talk is partially based on joint work with Erman Cineli and Viktor Ginzburg.

**14:00** Noah Porcelli (Cambridge)** ****Homotopical Lagrangian monodromy**** ***Abstract:* Given a Lagrangian submanifold L in a symplectic manifold X, a natural question to ask is: what diffeomorphisms f:L → L can arise as the restriction of a Hamiltonian diffeomorphism of X? Assuming L is relatively exact, we will extend results of Hu-Lalonde-Leclercq about the action of f on the homology of L, and deduce that f must be homotopic to the identity if L is a sphere or K(\pi, 1). The proof will use various moduli spaces of pseudoholomorphic curves as well as input from string topology. While motivated by HLL’s Floer-theoretic proof, we will not encounter any Floer theory.. **15:45** Ilaria Di Dedda (Londres)** A symplectic interpretation of Auslander algebras of type A.**

*Abstract:*

**The theme of this talk will be to build a bridge between two areas of mathematics: representation theory and symplectic geometry. Our objects of interest on the representation theoretical side (which I will define in this talk) are Auslander algebras of type A. This family of non-commutative algebras arises very naturally as endomorphism algebras of indecomposable modules of quivers of finite type. They were given a symplectic interpretation by Dyckerhoff-Jasso-Lekili, who proved the equivalence (as $A_{\infty}$-categories) between perfect derived categories of Auslander algebras of type A and certain partially wrapped Fukaya categories. We use their result to prove an equivalence between the categories in question and the Fukaya-Seidel categories of a certain family of Lefschetz fibrations. In this talk, we will observe this result in some key examples.**

Prochaines séances: 10 juin (?, ?, ?)

**Autre activité symplectique à Paris:**

**-**Séminaire Nantes-Orsay (à Orsay le 18 mars)

- Symplectic Zoominar (les vendredis hors symplectix à 15:15, heure de Paris)