Symplectix 4 décembre 2020

Exposés en ligne via BBB : http://bigbluebutton3.imj-prg.fr/b/cla-jeh-jn7

10h45 : Shira Tanny (Tel Aviv)

Title: The Poisson bracket invariant: elementary and hard approaches.

Abstract : In 2006 Entov and Polterovich proved that functions forming a partition of unity with displaceable supports cannot commute with respect to the Poisson bracket. In 2012 Polterovich conjectured a quantitative version of this theorem. I will discuss three interconnected topics: a solution of this conjecture in dimension two (with Lev Buhovsky and Alexander Logunov), a link between this problem and Grothendieck's theorem from functional analysis (with Efim Gluskin), and new results related to the Floer-theoretical approach to this conjecture (with Yaniv Ganor).

13h45 : Côme Dattin (Nantes) 

Titre : Wrapped sutured Legendrian homology and the conormal of braids

Abstract : In this talk we will describe some invariants of sutured Legendrians. A sutured contact manifold can be seen as either generalizing the contactisation of a Liouville domain, or as a presentation of a contact manifold with convex boundary.
Using the first point of view, we will define the wrapped sutured homology of Legendrians with boundary, employing ideas coming from Floer theory. 

To illustrate the second aspect, we apply the unit conormal construction  to braids with two strands, which yields a sutured Legendrian. 

We will  show that, for "local" braids, our sutured invariant is complete.
Thus  if the conormals of two 2-braids are Legendrian isotopic, the braids are  equivalent.