**11:00**Alexander Ritter (Oxford)

**The cohomological McKay correspondence via Floer theory**

*Abstract*: The goal of my talk is to present joint work with Mark McLean (Stony Brook, NY), which proves the cohomological McKay correspondence using symplectic topology techniques. This correspondence states that given a crepant resolution Y of the singularity \C^n / G, where G is a finite subgroup of SL(n,\C), the conjugacy classes of G are in 1-1 correspondence with generators of the cohomology of Y. This statement was proved by Batyrev (1999) and Denef-Loeser (2002) using algebraic geometry techniques. We instead construct a certain symplectic cohomology group of Y whose generators are Hamiltonian orbits in Y to which one can naturally associate a conjugacy class in G. We then show that this symplectic cohomology recovers the classical cohomology of Y.

**14:15**Francesco Lin (Princeton)

**Monopole Floer homology and spectral geometry**

*Abstract:*By studying the Seiberg-Witten equations, Kronheimer and Mrowka defined a package of invariants of three-manifolds called monopole Floer homology. In this talk, we discuss some interactions between this topological invariant and the spectral geometry of the Laplacian on the underlying Riemannian manifold, with the goal of understanding concrete examples of hyperbolic and Solv manifolds.

**16:00**Lucas Dahinden (Heidelberg)

**Volume growth of positive contactomorphisms**

*Abstract:*In cooriented contact manifolds there is a natural notion of moving positively, which gives birth to the notion of positive contactomorphism. The quest of studying the dynamical behaviour of these maps includes counting chords between special (Legendrian) submanifolds, which has implications for volume growth and topological entropy. The machinery we use is symplectic homology and Rabinowitz--Floer homology. In this talk I will try to avoid the heavy part of the machinery. Instead I focus on encoding geometric data in such an action functional, and on how to extract dynamical information.

Prochaines séances: 12/04 (Benedetti, Meschler, Golovko), 10/05 (Nonenmacher, Salamon, ?), 14/06 (Macarini, ?, ?).

**Autre activité symplectique à Paris:**

Séminaire Nantes-Orsay