Symplectix Vendredi 7 mai 2021

Séminaire actuellement dans le cadre du trimestre IHP.
Pour plus d'info voir ici: https://indico.math.cnrs.fr/event/5767/

10h45 : Baptiste Chantraine (Nantes)

Title : 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)

Title : 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 

Symplectix 2 avril 2021

 Séminaire à 10h45 puis à  13h45 en ligne via BBB : http://bigbluebutton3.imj-prg.fr/b/cla-jeh-jn7

10h45 : Johan Asplund (Uppsala)

Title : Chekanov-Eliashberg dg-algebras for singular Legendrians

Abstract : The Chekanov-Eliashberg dg-algebra is a holomorphic curve
invariant associated to a Legendrian submanifold of a contact manifold.
In this talk we explain how to extend the definition to singular
Legendrian submanifolds admitting a Weinstein neighborhood. Via the
Bourgeois-Ekholm-Eliashberg surgery formula, the new definition gives
direct geometric proof of the pushout diagrams and stop removal formulas
in partially wrapped Floer cohomology of Ganatra-Pardon-Shende. It
furthermore leads to a proof of the conjectured surgery formula relating
partially wrapped Floer cohomology to Chekanov--Eliashberg dg-algebras
with coefficients in chains on the based loop space. This talk is based
on joint work with Tobias Ekholm.

13h45 : Jonathan Zung (Princeton).

Title : Reeb flows transverse to foliations

Abstract : Eliashberg and Thurston showed that, roughly speaking, C^2 taut foliations on 3-manifolds can be approximated by tight contact structures. I will explain a new approach to this theorem which allows one to control the resulting Reeb flow and hence produce many hypertight contact structures. Along the way, I will explain how harmonic transverse measures may be used to understand the holonomy of foliations.