Symplectix 6 octobre 2023

Location: IHP, room 201 

10:45 Pazit Haim Kislev (Tel Aviv) 
Symplectic Barriers.
Abstract: The first example of a Lagrangian Barrier was introduced into symplectic geometry in 2001. It represents a symplectic rigidity phenomenon arising from necessary intersections with Lagrangian submanifolds which extend beyond mere topological considerations. Subsequently, numerous other instances of Lagrangian barriers have come to light.
In this joint work with Richard Hind and Yaron Ostrover, we present what appears to be the first illustration of Symplectic Barriers, a form of symplectic rigidity stemming from obligatory intersections of symplectic embeddings with symplectic submanifolds (and in particular not Lagrangian). In our work, we also tackle a question by Sackel–Song–Varolgunes–Zhu and provide bounds on the capacity of the ball after removing a codimension 2 hyperplane with a prescribed Kähler angle.

Gabriel Rivière (Nantes)
Poincaré series and linking of Legendrian knots.
On a compact surface of variable negative curvature, I will explain that the Poincaré series associated to the geodesic arcs joining two given points has a meromorphic continuation to the whole complex plane. Moreover, I will show that the value of Poincaré series at 0 can be expressed in terms of the linking of two Legendrian knots. I will also explain how this result extends when one considers geodesic arcs orthogonal to two fixed closed geodesics.
This is a joint work with N.V. Dang.

15:45 Ibrahim Trifa (Orsay)
Non-simplicity of some groups of area-preserving homeomorphisms in higher genus surfaces.
Abstract: In recent years, significant progress has been made in understanding the algebraic structure of the groups of area-preserving homeomorphisms of surfaces. In particular, in 2021 and 2022, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith have used Heegaard Floer Homology to introduce new spectral invariants and prove the non-simplicity of several groups in the case of the disc and the sphere. In this talk, I will present a generalization of their results in higher genus. This is joint work with Cheuk Yu Mak.

Next Symplectix:

10/11 (R. Avdek, L. Ioos, Y. Yao), 1/12, ...

Other symplectic activity in Paris:

- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time, first session of the year on Oct 13 with P. Seidel)

Symplectix 12 mai 2023

Warning: this will exceptionnally take place in Jussieu, room 15-16-101.  

This session is joint with the Jussieu dynamics seminar

Sheila Sandon (Strasbourg) 
Non-squeezing de contact à large échelle via les fonctions génératrices.

Abstract: En 2006 Eliashberg, Kim et Polterovich ont découvert un phénomène de non-squeezing en topologie de contact pour la variété R^2n x S^1 : ils ont montré (avec des techniques de SFT) que pour chaque nombre entier k il n'existe pas d'isotopie de contact qui envoie la prequantification d'une boule de R^2n de capacité plus grande de k dans la prequantification d'une boule de capacité plus petite de k. D'autre part, ils ont aussi montré qu'en dimension supérieure à 3 on peut toujours tasser la prequantification d'une boule de capacité inférieure à 1 dans la prequantification d'une autre boule arbitrairement petite, mais avaient laissé ouvert le cas général de boules de capacités supérieures à 1 pas séparées par des entiers ; le non-squeezing dans ce cas a été démontré par Chiu en 2017 avec les faisceaux et par Fraser en 2016 avec des techniques en continuité avec celles de Eliashberg, Kim et Polterovich. Dans mon exposé je vais présenter une démonstration de ce résultat général de non-squeezing avec les fonctions génératrices. Ceci est un travail en cours avec Maia Fraser et Bingyu Zhang..

Viktor Ginzburg (UC Santa Cruz)
Topological Entropy of Hamiltonian Systems and Persistence Modules.

Topological entropy is a fundamental invariant of a dynamical system,
measuring its complexity. In this talk, we will focus on connections between the topological entropy of a Hamiltonian dynamical system, e.g., a Hamiltonian diffeomorphism or a geodesic flow, and the underlying Morse or Floer homology viewed as a persistence module. We will recall the definition of barcode entropy — a Morse/Floer theoretic counterpart of topological entropy — and show that barcode entropy is closely related to topological entropy and that, for Hamiltonian diffeomorphisms and geodesic flows in low dimensions, these invariants are equal. Time permitting, we will also touch upon possible ways to extend these definitions and results to Reeb flows. The talk is based on joint work with Erman Cineli, Basak Gurel and Marco Mazzucchelli.

15:45 Frédéric Le Roux (Jussieu)
Le groupe des automorphismes du graphe fin des courbes d'une surface.

Abstract: Lan, Margalit, Pham, Verbene et Yao ont montré en 2021 que le groupe des automorphismes du graphe fin des courbes d'une surface de genre au moins
2 s'identifie au groupe des homéomorphismes de la surface. Avec Maxime Wolff, nous généralisons ce résultat à toute surface, et nous en décrivons la version lisse. Les liens entre le graphe fin et la dynamique ont été récemment explorés par Bowden, Hansel, Militon, Man, et webb dans le cas du tore, et généralisés par Guihéneuf et Militon en genre supérieur..

Other symplectic activity in Paris:
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)

Symplectix 7 avril 2023

Location: IHP, room 201 

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

Gabriele Benedetti (Amsterdam) 
Zoll magnetic flows on the two-torus: a Nash-Moser construction.
Abstract: In recent years, tools from contact and symplectic geometry have been very effective in studying systolic questions arising from metric and convex geometry. In particular, under general assumptions the local maximizers of the systolic ratio are Zoll flows, namely those flows generating a free circle action. Therefore, it is interesting to construct Zoll flows in specific classes of systems. In 1976, Guillemin used the Nash-Moser implicit function theorem to construct an infinite-dimensional family of Zoll geodesic flows on the two-sphere close to the round metric. In this talk, we build on Guillemin's idea and we construct an infinite-dimensional family of integrable Zoll magnetic flows on the two-torus, a case which presents new analytical difficulties. This is joint work in progress with Luca Asselle and Massimiliano Berti.

Arnaud Maret (Jussieu)
Action-angle coordinates for character varieties à la Kapovich--Millson.
We study a moduli space of triangle chains in the hyperbolic plane with prescribed angles and relate it to a character variety of surface group representations in PSL(2,R). We will explain how to describe action-angle coordinates on the above-mentioned moduli space for the Goldman symplectic structure. There is a natural action of a mapping class group that preserves the symplectic structure. We will see that this action is ergodic. .

15:45 Théo Marty (Bonn)
Reeb-Anosov flows in dimension 3.

Abstract: Geodesic flows are important examples of both Reeb flows and Anosov
flows (on hyperbolic surfaces). Others Reeb-Anosov flows have been
constructed by Dehn surgery on already existing Reeb-Anosov flows. But
the set of Reeb-Anosov flows was not well understood until recently. I
will present of combination of recent results: an Anosov flow is
topologically equivalent to a Reeb-Anosov flow if and only if it admits
an open book decomposition, if and only if its orbit space is R-covered
and skewed..

Next Symplectix:


Other symplectic activity in Paris:

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