Three 20 minute research talks

Zoom link:  :  https://umontreal.zoom.us/j/94366166514?pwd=OHBWcGluUmJwMFJyd2IwS1ROZ0FJdz0

Alexandre Jannaud,
 University of Neuchâtel   Dehn-Seidel twist, C^0 symplectic geometry and barcodes

In this talk I will present my work initiating the study of the $C^0$ symplectic mapping class group, i.e. the group of isotopy classes of symplectic homeomorphisms, and briefly present the proofs of the first results regarding the topology of the group of symplectic homeomorphisms. For that purpose, we will introduce a method coming from Floer theory and barcodes theory. Applying this strategy to the Dehn-Seidel twist, a symplectomorphism of particular interest when studying the symplectic mapping class group, we will generalize to $C^0$ settings a result of Seidel concerning the non-triviality of the mapping class of this symplectomorphism. We will indeed prove that the generalized Dehn twist is not in the connected component of the identity in the group of symplectic homeomorphisms. Doing so, we prove the non-triviality of the $C^0$ symplectic mapping class group of some Liouville domains.

Tim Large, Massachusetts Institute of Technology,    Floer K-theory and exotic Liouville manifolds

In this short talk, I will explain how to construct Liouville manifolds which have zero traditional symplectic cohomology but interesting symplectic K-theory. In particular, we construct an exotic symplectic structure on Euclidean space which is not distinguished by traditional Floer homology invariants. Instead, it is detected by a module spectrum for complex K-theory, built as a variant of Cohen-Jones-Segal’s Floer homotopy type. The proof involves passage through (wrapped) Fukaya categories with coefficients in a ring spectrum, rather than an ordinary ring.

Oliver Edtmair, University of California, Berkeley   3D convex contact forms and the Ruelle invariant

Is every dynamically convex contact form on the three sphere convex? In this talk I will explain why the answer to this question is no. The strategy is to derive a lower bound on the Ruelle invariant of convex contact forms and construct dynamically convex contact forms violating this lower bound.

This is based on joint work with Julian Chaidez.