This is a working group seminar run by Klaus Mohnke and Chris Wendl on recent developments in symplectic geometry. 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.
The seminar will meet this semester mainly on Mondays at 15:00 (c.t.) in room 1.315 (Rudower Chaussee 25). There will also be occasional meetings on Tuesdays at 11:00 (c.t.).
Note that on three Mondays this semester (April 24, May 22 and June 26), the seminar will not meet due to the Berlin-Hamburg Symplectic Geometry Seminar.
| Tuesday April 18, 2017 11:00-13:00 (c.t.) RUD 25, Room 4.007 |
initial meeting to discuss further plans |
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| Monday April 24, 2017 14:30-17:00 (s.t.) RUD 25, Room 3.008 |
Berlin-Hamburg Symplectic Geometry Seminar with speakers Steven Sivek (MPI Boon) and Paolo Ghiggini (Université de Nantes) |
| Tuesday April 25, 2017 11:00-13:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Paolo Ghiggini (Université de Nantes) Topic: Cthulhu meets Dr. Frankenstein Abstract: I will revise the definition of Floer homology for Lagrangian cobordisms and show how it can be used to reprove that Lagrangian surgery on exact Lagrangian submanifolds corresponds to a mapping cone of their Floer complexes. This is joint work with Baptiste Chantraine, Georgios Dimitroglu Rizell and Roman Golovko. (Note: this talk is a supplement to Ghiggini's talk the previous day in the Berlin-Hamburg Symplectic Geometry Seminar) |
| Monday May 1, 2017 | NO SEMINAR THIS WEEK (holiday) |
| Monday May 8, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Viktor Fromm Topic: Symplectic homology and divisor sums Abstract: Originally divised and applied by Gompf in the closed case, the symplectic sum construction can be used in order to attach a closed symplectic manifold to a symplectic domain along a common symplectic hypersurface. For example, the complement of a symplectic hypersurface in a closed symplectic manifold may be viewed as (a trivial case of) a divisor sum of this type. The goal of the talk is to explain a long exact sequence for computing in favorable cases the (positive) symplectic homology of such a divisor sum in terms of a Gromov-Witten invariant of the closed manifold and a (suitably defined positive) symplectic homology of the original symplectic domain. |
| Monday May 15, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Viktor Fromm Topic: Symplectic homology and divisor sums (continued) |
| Monday May 22, 2017 | NO SEMINAR THIS WEEK due to Berlin-Hamburg Symplectic Geometry Seminar (in Hamburg) with speakers Doris Hein (Freiburg) and Jo Nelson (Columbia/IAS) |
| Monday May 29, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Viktor Fromm Topic: Symplectic homology and divisor sums (continued) |
| Monday June 5, 2017 | NO SEMINAR THIS WEEK (holiday) |
| Monday June 12, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Agustin Moreno Topic: Algebraic torsion in higher-dimensional contact manifolds |
| Monday June 19, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Agustin Moreno Topic: Algebraic torsion in higher-dimensional contact manifolds (continued) |
| Monday June 26, 2017 14:30-17:00 (s.t.) RUD 25, Room 2.006 |
Berlin-Hamburg Symplectic Geometry Seminar with speakers Kyler Siegel (MIT) and Vsevolod Shevchishin (Olsztyn) |
| Tuesday June 27, 2017 10:00-12:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Kyler Siegel (MIT) Topic: Squared Dehn twists, symplectic fragility, and bulk deformations Abstract: Classical Dehn twists are self-diffeomorphisms of surfaces which are supported near closed curves. These generalize to higher dimensions as symplectomorphisms of symplectic manifolds which are supported near Lagrangian spheres. In dimension four, Seidel observed that squared Dehn twists exhibit a strange phenomenom called "fragility", which means that they become trivial after arbitrarily small perturbations of the symplectic form. Although this phenomenon has no obvious geometric meaning in higher dimensions, I will formulate and prove a higher dimensional analogue using the notion of a "bulk deformed" Fukaya category. As an application, I will explain how this implies various computations of twisted and bulk deformed symplectic cohomologies for the subflexible examples constructed by Murphy and the speaker. |
| Monday July 3, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Sarah Geiß Topic: Introduction to Khovanov homology |
| Monday July 10, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Alex Fauck Topic: Subcritical handle attachment |
| Monday July 17, 2017 15:00-17:00 (c.t.) RUD 25, Room 1.315 |
Speaker: Alex Fauck Topic: Constructing new fillable contact manifolds via connected sums |