Lieu: IHP, salle 201.
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
