From to

Shedule -

2021-T2 Symplectic topology, contact topology and interactions

Symplectic topology, contact topology and interactions, Paris

IHP
Amphithéatre Darboux
Paris

Thematic trimester program at Institut Henri Poincaré, Paris (Back to main page)

It has been more than 25 years ago that the previous thematic program on symplectic topology took place at Institut Henri Poincaré. Since then, the field has undergone a spectacular transformation earning itself a central position in the mathematical landscape. It interacts strongly with other fields such as dynamical systems, low dimensional topology, homotopical algebra, and algebraic geometry.

Main events:

Weekly seminar & other activities

Zoom link:

https://us02web.zoom.us/j/86503014755?pwd=Q2tkQ2gwNXVqNU5RT3crWHo2SmJxUT09

 

  • Friday June 18th : Symplectic online seminar

10h45 : Sushmita Venugopalan (IMSc Chennai) : Tropical Fukaya Algebras

Abstract: A multiple cut operation on a symplectic manifold produces a collection of cut spaces, each containing relative normal crossing divisors. We explore what happens to curve count-based invariants when a collection of cuts is applied to a symplectic manifold. The invariant we consider is the Fukaya algebra of a Lagrangian submanifold that is contained in the complement of relative divisors. The ordinary Fukaya algebra in the unbroken manifold is homotopy equivalent to a `broken Fukaya algebra' whose structure maps count `broken disks' associated with rigid tropical graphs. Via a further  degeneration, the broken Fukaya algebra is homotopy equivalent to a `tropical Fukaya algebra' whose structure maps are sums of products over vertices of tropical graphs. This is joint work with Chris Woodward.

 

13h45 : Steven Sivek (Imperial College London) : TBA

Abstract: TBA
 
  • Friday June 11th : Symplectic online seminar

10h45 : Pierre Dehornoy (U. Grenoble Alpes) : The genus-one question for open book decomposition

Abstract: In dimension 3, every contact structure is supported by an open book decomposition. When the structure is overtwisted one can strengthen the statement and have an OBD with genus-zero pages. For tight structures, there are many examples of OBD with genus-one pages, and Etnyre asked around 2006 whether it always exists. The question is still open. I will discuss a parallel and related question, for Anosov flows instead of contact structures. I will explain some constructions of genus-one OBD, and report on a partial result for OBD with genus-two pages (with the assistance of a computer).

 

13h45 : Octav Cornea (U. de Montréal) : Triangulation and persistence

Abstract: Mixing triangulation (in the sense of triangulated categories) with persistence
(as in persistence modules) leads to a class of interesting pseudo-metrics in a variety
of examples: metric spaces, Tamarkin categories, filtered topological spaces, Fukaya
categories. I will discuss some generalities concerning this machinery and how it
specifically applies to the symplectic context. The talk is based on joint work with
Paul Biran (ETH) and Jun Zhang (CRM). 
 
  • Friday June 4th : Symplectic online seminar

10h45 : Alfonso Sorrentino (U. Rome Tor Vergata) : Rigidity phenomena in Billiard and Hamiltonian Dynamics

Abstract: In this talk I shall address several rigidity questions appearing in the study of  billiard maps and Hamiltonian dynamical systems, with a particular focus on their integrability and their action-spectral properties.

 

13h45 : Yusuke Kawamoto (ENS & Sorbonne Université) : Around a Question of Entov-Polterovich-Py

Abstract: In this talk I will discuss a celebrated question posed by Entov, Polterovich and Py on quasimorphisms. First I will explain my partial answer to this question which is based on my preprint and then I will explain other phenomena related to this topic which is a joint work with Egor Shelukhin.
 
  • Friday May 28th : Symplectic online seminar

10h45 : Alberto Abbondandolo (Bochum) : Bi-invariant Lorentz-Finsler structures on the linear symplectic group and contactomorphism group

Abstract: It is well known that the linear symplectic group and the contactomorphism group do not admit any bi-invariant metric which is compatible with the Lie group topology. In this talk, I will discuss two mutually related bi-invariant Lorentz-Finsler structures on these groups. The talk is based on some work in progress with Gabriele Benedetti and Leonid Polterovich.

 

13h45 : Marco Mazzucchelli (ENS Lyon) : A few properties of Besse contact manifolds.

Abstract : A closed connected contact manifold is called Besse when all of its Reeb orbits are closed, and Zoll when furthermore all Reeb orbits have the same minimal period. In this talk, I will present a recollection of recent results/work in progress on the subject:
- It is known that Besse contact 3-spheres are strictly contactomorphic to rational ellipsoids. In higher dimensions, the analogous statement is open. Nevertheless, I will show that at least those contact (2n-1)-spheres that are convex hypersurfaces in symplectic vector spaces still "resemble" a rational ellipsoid. This is joint work with Marco Radeschi.
- Inspired by recent results on the systolic optimality of Zoll contact manifolds, I will show that Besse contact 3-manifolds are local maximizers of a suitable generalized systolic ratio. This is joint work with Alberto Abbondandolo and Christian Lange.

  • Friday May 7th : Symplectic online seminar

10h45 : Baptiste Chantraine (Nantes) : compact objects in the Fukaya category and representations of Eliashberg-Chekanov algebra.

Abstract : Let L be a compact Lagrangian in a Weinstein manifold obtained from a subcritical one by attaching a handle along a Legendrian V. We will see how to associate to L a filling of a satelite of V and how this one induces a representation of the Chekanov-Eliashberg algebra of V. We will show that Legendrian contact homology linearised with respect to this representation recovers the Floer homology of L. We will talk about extensions of this considerations to A-infinity opérations on both sides. This is a joint work with G. Dimitroglou-Rizell and P. Ghiggini
 

13h45 : Paolo Ghiggini (Nantes) : Many real projective spaces are not Liouville fillable

Abstract : I will show that the standard contact structure on the real projective spaces RP^{4k+1} is not Liouville fillable using a classical argument on degeneration of moduli spaces of holomorphic spheres. A stronger result has been obtained by Zhengyi Zhou using more algebraic methods. This is a joint work with Klaus Niederküger 

  • Tuesday May 4th : Graduate student day at IHP
     
10h-12h Groupe de travail doctorants - Amphi Darboux
15h-18h Exposés des doctorants - Amphi Darboux 


 

Organizing committee:

Jean-François Barraud (Toulouse) Hélène Eynard-Bontemps (Paris)
Frédéric Bourgeois (Orsay) Patrick Massot (Orsay)
Vincent Colin (Nantes) Klaus Niederkrüger (Lyon)
Sylvain Courte (Grenoble) Alexandru Oancea (Paris)
Vincent Humilière (École Polytechnique) Sobhan Seyfaddini (Paris)
Mihai Damian (Stasbourg) Anne Vaugon (Orsay)
   

Scientific committee:

Denis Auroux (Harvard) Yasha Eliashberg (Stanford)
Paul Biran (Zurich) Helmut Hofer (IAS Princeton)
Tobias Ekholm (Uppsala) Dusa McDuff (Columbia)

 


Program coordinated by the Centre Emile Borel at IHP Sorbonne Université, CNRS.

            

also supported by:

           

 

You also, comment on this article
Choose an avatar :
(For reasons of confidentiality, avoid entering a pseudonym allowing you to identify yourself)