Location: IHP, room 201

The talks are broadcasted via Zoom:

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

**9:30** Matija Sreckovic (ENS)** Link between Flow Categories of Morse Functions and FukayaCategories of Lefschetz Fibrations on the Cotangent Bundle.**

*Abstract*: I will start the talk by explaining some concepts used in Emmanuel

Giroux's construction of a Lefschetz fibration on the cotangent bundle

which extends a given Morse function on the zero section. I will then

state a variant of a conjecture by Paul Seidel on a link between the flow

category of the Morse function and the directed Donaldson-Fukaya category

of the Lefschetz fibration. In the main part of the talk, I will explain

how to prove this conjecture in dimension 2, and some progress I've made

in dimension 3. The main tool in the proof is an explicit handle

decomposition of the real regular fibers of the Lefschetz fibration, which

allows us to see what the vanishing cycles look like.

**10:45** Simon Vialaret (Bochum and Orsay)** Systolic inequalities for S^1-invariant contact forms.**

*Abstract*: In Riemannian geometry, a systolic inequality aims to give a uniform bound on the length of the shortest closed geodesic for metrics with fixed volume on a given manifold. This notion generalizes to contact geometry, replacing the geodesic flow by the Reeb flow, and the length by the period. As opposed to the Riemannian case, it is known that there is no systolic inequality for general contact forms on a given contact manifold. In this talk, I will state a systolic inequality for contact forms that are invariant under a circle action in dimension 3, and give applications to Finsler geodesic flows and to a conjecture of Viterbo.

**14:00** Adrien Currier (Nantes)

About the nearby Lagrangian conjecture in locally conformally symplectic geometry.*Abstract: *Locally conformally symplectic (lcs) geometry is a generalization of symplectic geometry in which a manifold is endowed with a non-degenerate 2-form that is locally a symplectic form up to some positive factor. If the local behavior of such a manifold is largely identical to that of a symplectic manifold, the global behavior can nonetheless vastly differ. For example, while it is possible to define Lagrangian submanifolds in lcs geometry, we also have to contend with the fact that S^3 \times S^1 has a canonical "exact" lcs structure given by the canonical contact form of S^3 through a process known as circular lcs-ization.

The foremost goal of this talk will be to familiarize the public with lcs geometry and its ties to other branches geometry, most notably contact geometry. To do this, I will use a couple of results I have obtained during my thesis as a narrative thread. These results will focus on the nearby Lagrangian conjecture in lcs geometry and, more specifically, on the possibility of an lcs adaptation of the Abouzaid-Kragh theorem.

**Other symplectic activity in Paris:**

-** **Séminaire Nantes-Orsay

- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)

- Soutenance de thèse de Francesco Morabito le 26 juin à 16h, Ecole Polytechnique, amphi Becquerel.