HOLOMORPHIC METHODS IN SYMPLECTIC GEOMETRY

12 - 14 February 2018
Ruprecht-Karls-Universität Heidelberg

Lecture series by
Dietmar Salamon (ETH Zürich) — Geometric invariant theory in finite and infinite dimensions
Kai Zehmisch (Gießen) —The filling-by-holomorphic-discs method

Hansjörg Geiges (Köln), Samuel Trautwein (ETH Zürich) and Will Merry (ETH Zürich)

All talks will take place at the University of Heidelberg,
in the Maths building (Mathematikon) on the ground floor,
in the Hörsaal.
Directions

 Schedule Monday 9:00 - 10:30 Kai Zehmisch — $\Gamma_4=0$ Coffee break 11:30 - 13:00 Dietmar Salamon — GIT and the moment map I (The moment-weight inequality) Lunch break 15:00 - 16:00 Hansjörg Geiges — $\Gamma_3=0$ Coffee break 17:00 - Visit Heidelberg Palace and workshop dinner at the Restaurant Zum güldenen Schaf Tuesday 9:00 - 10:30 Dietmar Salamon — GIT and the moment map II (The Hilbert-Mumford criterion) Coffee break 11:30 - 12:30 Samuel Trautwein — Gauge groups, moment maps, and the symplectic vortex equation Lunch break 14:00 - 15:30 Kai Zehmisch — $S^3$ holomorphic Coffee break 16:30 - 17:30 Will Merry — Floer homology and contact Hamiltonians Wednesday 9:00 - 10:30 Kai Zehmisch — Extending over the ball Coffee break 11:30 - 13:00 Dietmar Salamon — Diffeomorphism groups, complex structures, and the Ricci form Lunch / departure

Participation is open. Participants are kindly requested to send an e-mail to Mrs Nicole Umlas (numlas "at" mathi.uni-heidelberg.de) not later than Monday, January 29, 2018. Please indicate whether you wish to participate in the conference dinner on Monday. If you want us to book a hotel room, please mention this in your e-mail to Mrs Umlas. We may have some funds to support the hotel costs.

This meeting is supported by the DFG through SFB/TRR 191 - Symplectic Structures in Geometry, Algebra and Dynamics and RTG 2229 - Asymptotic Invariants and Limits of Groups and Spaces .

Lecture Notes:

Dietmar Salamon - Lecture 1 , Lecture 2

Hansjörg Geiges - $\Gamma_3=0$

Kai Zehmisch - The filling-by-holomorphic-discs method

Abstracts:

Kai Zehmisch — The filling-by-holomorphic-discs method

In 1968 Cerf proved his celebrated result stating that all diffeomorphisms of the 3-sphere extend to a diffeomorphism of the 4-ball. Based on his classification of contact structures on the 3-sphere Eliashberg proposed in 1992 to use Gromovʼs holomorphic curves technique to give a contact theoretic proof of Cerfʼs theorem. In this lecture series I will present the analytic details of Eliashbergʼs proof of Cerfʼs theorem based on a joint paper with Geiges from 2010.
In lecture 1 I will show how to reduce Cerfʼs theorem to symplectic geometry via Eliashbergʼs classification theorem. In lecture 2 main concepts from contact geometry will be introduced in order to understand the standard holomorphic disc filling of the 3-sphere. In lecture 3 I will demonstrate how analytic tools from elliptic PDEs can be used for an actual extension of a given diffeomorphism of the 3-sphere.

Hansjörg Geiges — $\Gamma_3=0$

In this talk I will provide some differential topological background for the lectures by Zehmisch. In particular, I will outline Smale's proof that the diffeomorphism group of the 2-sphere retracts to the group of isometries.