# Symplectic geometry seminar

## Spring Semester 2017

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
20 February 2017
15:15-16:30
no seminar HG G 43
27 February 2017
15:15-16:30
Claire Voisin
Jussieu and ITS
Hyper-Kähler manifolds and their moduli HG G 43
6 March 2017
15:15-16:30
Felix Schlenk
Université de Neuchâtel
HG G 43
Abstract: We look at the following chain of symplectic embedding problems in dimension four. E(1,a) \to Z^4(A), E(1,a) \to P(A,bA) (b \in \NN), E(1,a) \to T^4(A). Here $E(1,a)$ is a symplectic ellipsoid, $Z^4(A)$ is the symplectic cylinder $D^2(A) \times R^2$, $P(A,bA) = D^2(A) \times D^2(bA)$ is the polydisc, and $T^4(A) = T^2(A) \times T^2(A)$, where $T^2(A)$ is the torus of area $A$. In each problem we ask for the smallest $A$ for which $E(1,a)$ symplectically embeds. The answer is very different in each case: total rigidity, total flexibility, and a two-fold subtle transition between them. The talk is based on works by Cristofaro-Gardiner, Frenkel, Latschev, McDuff, Müller and myself.
13 March 2017
15:15-16:30
Samuel Trautwein
ETH Zürich
HG G 43
Abstract: The symplectic vortex equations admit a variational description as global minimum of the Yang--Mills--Higgs functional. We discuss convergence of its gradient flow on holomorphic pairs and explain how this can be used to obtain several results inspired by finite dimensional GIT: The analogue of the Ness uniqueness theorem, the moment-weight inequality, the Kempf existence and uniqueness theorem and an extension of Mundet's Kobayashi--Hitchin correspondence to the polystable and semistable case.
20 March 2017
15:15-16:30
Charel Antony
ETH Zürich
HG G 43
Abstract: In connecting two Morse functions on a manifold by a smooth family of functions, the concept of birth-death critical points (BDCP) appears naturally. On the level of critical points, we see two critical points running into each other and then disappearing (or dying) as we vary the parameter near the BDCP. After some definitions and a normal form for BDCP, we will discuss the existence and uniqueness of gradient flow lines connecting the two critical points near such a BDCP and how adiabatic limit techniques enter in the analysis of the problem.
27 March 2017
15:15-16:30
no seminar HG G 43
3 April 2017
15:15-16:30
Claude Viterbo
ENS Paris
HG G 43
Abstract: We explain how, given an exact spin Lagrangian $L$, in $T^*N$, Floer homology and rectification of quasi-presheaves allow one to construct a sheaf $F_L$ on $N\times R$ with singular support the conification of $L$. We show how filtered Floer homology of $L_1,L_2$ is recovered from the sheaves $F_{L1}, F_{L_2}$.
10 April 2017
15:15-16:30
Dr. Doris Hein
Universität Freiburg
HG G 43
Abstract: Local homology is a useful tool to study periodic orbits. For example, the key to the existence of infinitely many periodic orbits of Hamiltonian systems are properties of the local Floer homology of one special orbit. I will discuss a discrete version of this invariant constructed using local invariant Morse homology of a discrete action function. The construction is very geometric and relies on a hands-on description of invariant local Morse homology. The resulting local homology can be interpreted as an invariant of germs of Hamiltonian systems or of closed Reeb orbits. It has properties similar to those of local Floer homology in the symplectic setting and probably similar applications in dynamics.
17 April 2017
15:15-16:30
no seminar (easter monday) HG G 43
24 April 2017
15:15-16:30
no seminar (sechselaeuten) HG G 43
1 May 2017
15:15-16:30
no seminar (tag der arbeit) HG G 43
8 May 2017
15:15-16:30
Prof. Dr. William John Merry
ETH Zurich, Switzerland
Maximum Principles in Symplectic Homology HG G 43
15 May 2017
15:15-16:30