logo naam

Mini-Workshop on Symplectic Geometry, Utrecht University, March 11, 2016

Titles and abstracts for the talks

Janko Latschev:
Homological algebra related to Riemann surfaces with boundary

I will motivate an algebraic framework which appears in three different but related contexts: (S^1-equivariant) string topology, symplectic field theory and Lagrangian Floer theory. The relevant algebraic structure is a homotopy version of involutive bi-Lie algebras, which will be introduced in detail. The talk is based on joint work with Kai Cieliebak and Kenji Fukaya.

Yaron Ostrover:
Symplectic measurements of convex sets

We will discuss some computational aspects of symplectic capacities for convex sets in the classical phase space. In particular, we will explain relations with billiard dynamics, and show how a symplectic isoperimetric conjecture by Viterbo is related to a 70-years old open conjecture by Mahler regarding the volume product of convex sets. The talk is based on joint works with Shiri Artstein-Avidan, Efim Gluskin, and Roman Karasev.

Fabian Ziltener:
Leafwise fixed points for $C^0$-small Hamiltonian flows and local coisotropic Floer homology

Consider a symplectic manifold $(M,\omega)$, a closed coisotropic submanifold $N$ of $M$, and a Hamiltonian diffeomorphism $\phi$ on $M$. A leafwise fixed point for $\phi$ is a point $x\in N$ that under $\phi$ is mapped to its isotropic leaf. These points generalize fixed points and Lagrangian intersection points. The main result of this talk will be that $\phi$ has a leafwise fixed point, provided that it is the time-1-map of a Hamiltonian flow whose restriction to $N$ stays $C^0$-close to the inclusion $N\to M$. This result is optimal in the sense that the $C^0$-condition cannot be replaced by the assumption that $\phi$ is Hofer-small. The method of proof of this result leads to a local coisotropic version of Floer homology.

Claude Viterbo, colloquium talk:
Spectral invariants and C^0 symplectic topology

We shall explain how symplectic invariants allow us to ``measure'' the size of sets or maps in symplectic topology. This is a very flexible tool, that allows to prove a number of classical rigidity results in symplectic topology, and also, more recently, some results on area preserving maps of surfaces.

Claude Viterbo, second talk:
Sheaves in symplectic topology

We shall explain the connection between microlocal theory of sheaves and symplectic topology, and also what type of new interactions one could hope for.