Symplectix 4 avril 2025

 

Location: IHP, room 201

The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

 

10:45 Adrian Petr (Odense)
A universal characterization of the curved A-infinity operad.
Abstract: According to Floer theory, a Lagrangian L in a symplectic manifold gives rise to a curved A-infinity algebra CF(L). In operadic language, we say that CF(L) is an algebra over the curved A-infinity operad.
In this talk, we will introduce a category `Curv' of operads equipped with a distinguished curvature term.  We determine the initial element: it is the curved A-infinity operad -- thus giving a universal characterization of this structure.
We then show that the operadic twisting procedure comes from the adjunction for the forgetful functor from Curv to operads over A-infinity.  For symmetric operads, the same ideas characterize the curved L-infinity operad and the corresponding twisting procedure.
This is based on joint work with Guillaume Laplante-Anfossi and Vivek Shende..

14:00 Robin Riegel (Strasbourg)   
A Morse theoretical approach to the Chas-Sullivan product.
Abstract:  Barraud, Damian, Humilière and Oancea introduced Morse Homology with differential graded coefficients which they show to be a particularly adapted framework to give a finite dimensional approach to study the homology of total spaces of fibrations over a closed manifold. We will discuss how this new theory enables to build a model for (and generalize) a fundamental operation in string topology, the Chas-Sullivan product on the free loop space of a closed manifold.
 

15:45 Shuo Zhang (Beijing)
Composed Dehn twist exact sequence through A infinity n-modules.
Abstract: We prove the quilted Floer cochain complexes form A infinity n-modules over the Fukaya category of Lagrangian correspondences.  Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex can be identified with bar complex from ordinary Floer theory.  As an application we use a family version of quilt unfolding argument to prove two long exact sequences conjectured by Seidel that relates the Lagrangian Floer cohomology of a collection of (possibly intersecting) Lagrangian spheres and the fixed point Floer cohomology of composition of Dehn twists along them. .

Next symplectix:

6/06

Other symplectic activity in Paris (and in France):

- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays at 15:15 (except Symplectix' Fridays) Paris time)

Symplectix 7 mars 2025

Location: IHP, room 201

The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

 

10:45 Rohil Prasad (Berkeley)   
Invariant sets in three-dimensional energy surfaces.
Abstract: Let H be any smooth function on R^4 and let Y be any compact and regular level set. I'll explain a proof that Y admits an infinite family of proper compact subsets that are invariant under the Hamiltonian flow, which in addition have dense union in Y. This improves on a 2018 result by Fish-Hofer.

14:00 Shah Faisal (Strasbourg)   
Extremal Lagrangian tori in toric domains.
Abstract:  The symplectic area of a Lagrangian submanifold L of a symplectic manifold is defined to be the minimal positive symplectic area of a smooth 2-disk with boundary on L.   An extremal Lagrangian torus is a Lagrangian torus that maximizes the symplectic area among the Lagrangian tori.  In this talk, I will explain that every extremal Lagrangian torus in the standard symplectic unit ball is entirely contained in the boundary of the ball. This answers a question attributed to Lazzarini and settles a conjecture of Cieliebak and Mohnke in the affirmative.
 

15:45 Amanda Hirschi (Jussieu)
Open Gromov-Witten invariants and Lagrangian cobordism.
Abstract: I will describe a construction of open Gromov-Witten invariants in genus zero for embedded (relatively spin) Lagrangians. This uses the framework of Solomon-Tukachinsky and a construction of global Kuranishi charts for moduli space of stable maps with Lagrangian boundary condition. I will describe the invariance of this numbers and how they are related under Lagrangian cobordisms. This is work in progress, joint with Kai Hugtenburg.

Next symplectix:

4/04 (Petr, Riegel, Zhang), 6/06

Other symplectic activity in Paris (and in France):

- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays at 15:15 (except Symplectix' Fridays) Paris time)

Symplectix 10 janvier 2025

Location: IHP, room 201

The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

 

10:45 Vivek Shende (Odense)  
A topological classification of generating functions.
Abstract: From a generating function for a Legendrian in a 1-jet bundle, one may extract the following topological information: (1) a trivialization of the stable Gauss map, (2) the sheaf of sub-level-set stable cohomotopies, and (3) an identification of the microlocalization of the latter with the J-homomorphism image of the former. Here we show that in fact (1), (2), (3) completely classify generating functions up to the natural equivalence relations of stabilization and fiberwise diffeomorphism.
This talk presents joint work with Sylvain Courte.

14:00 Oğuz Şavk (Nantes)  
Homology concordances and links of isolated singularities of complex hypersurfaces.
Abstract:  In this talk, I will present my ongoing joint work with Marco Golla on the study of the homology concordance group, one of the high-dimensional generalizations of the concordance group to homology spheres and homology cobordisms. In particular, I will discuss the subgroup generated by links of Brieskorn-Pham singularities (which can be thought of as high-dimensional torus knots).
 

15:45 Seungook Yu (Nantes)
Contact instantons and its Legendrian Floer cohomology in one-jet bundle.
Abstract: In the study of Floer theory in contact geometry, symplectization has been widely used. However, the symplectization process may result in the loss of geometric or topological information inherent to the given contact manifold. To address this, it is necessary to develop Floer theory directly on contact manifolds without relying on symplectization. Contact instantons have been introduced as a tool to achieve this goal. In this talk, I will introduce contact instantons and use them to define Legendrian Floer cohomology for Legendrian submanifolds that are Hamiltonian isotopic to the zero section in one-jet bundles. If time permits, I will also discuss the construction of spectral invariants as an application. This is a joint work with Yong-Geun Oh. .

Next symplectix:

7/03, 4/04

Other symplectic activity in Paris (and in France):

- CAST 2025 Workshop (6-8 February in Grenoble)
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays at 15:15 (except Symplectix' Fridays) Paris time)