Research Seminar: Symplectic Geometry (SS 2022)

This is a working group seminar run by Klaus Mohnke, Chris Wendl, and Thomas Walpuski on recent developments in symplectic geometry and related areas. Participants are expected to be familiar with the basics of symplectic geometry, including some knowledge of holomorphic curves and/or Floer-type theories. The seminar is conducted in English.

Time: Mondays 13-15 (starting on 2022-04-25)
Location: Johann von Neumann-Haus (Rudower Chaussee 25) Seminarraum 30 3.007
Moodle page (key: gromov)

Conformal symplectic foliations on closed manifolds
Eliashberg and Thurston discovered in '98 a surprising relationship between foliations and contact structures in dimension 3: (most) C^2 foliations can be C^0-approximated by contact structures; there are moreover interesting connections between their properties. In higher dimensions, the best candidates for such type of results seem to be (codimension 1) foliations equipped with a conformal symplectic leafwise structure, according to recent results by Bertelson and Meigniez on manifolds with non-empty boundary. In this talk, I will give an introduction to this and related problematics, and present a work joint with Lauran Toussaint where we prove the existence of conformal symplectic foliations on closed manifolds of odd dimension at least 7 in any given almost contact class using the h-principle of Bertelson--Meigniez. Time permitting, I will also discuss the existence of conformal symplectic and symplectic foliations on simply connected 5-dimensional manifolds.
Notions of torsion in SFT and RSFT, I
In the first talk of this two-part series, I will give a rough outline of the algebraic structure of (full and rational) symplectic field theory, and recount some of the history of its use for constructing invariants that obstruct symplectic fillings and cobordisms between contact manifolds.
Notions of torsion in SFT and RSFT, II
In the second talk, I will sketch the recent contributions to this subject by Moreno and Zhou, who have introduced the first (as far as I'm aware) geometric application based specifically on rational SFT.
Shah Faisal
Naageswaran Manikandan
Laurenz Upmeier zu Belzen

Note for new students: If you think you might be interested in this seminar but have neither attended before nor spoken with Profs. Mohnke, Wendl, or Walpuski about it, it is a good idea to get in touch with one of us ahead of time!