Lieu: IHP, salle 314.
The seminar will take place in presence, but will be broadcasted via zoom
https://us02web.zoom.us/j/85370013931?pwd=T2JBN2FtNExiNVRkYzBCMVhDU1d6Zz09
10:45 Mathias Meiwes (Aachen)
Hofer's geometry, braid stability and entropy.
Abstract: A central object in the study of Hamiltonian diffeomorphisms on a
symplectic manifold is Hofer's metric, a bi-invariant metric on the
group of Hamiltonian diffeomorphisms, and interesting questions circle
around the link of Hofer's geometry to dynamical properties
of those diffeomorphisms. In my talk I will discuss results on stability features of
topological entropy of a Hamiltonian diffeomorphism with respect to
Hofer's metric. One result that I will discuss, and which was recently obtained together
with Marcelo Alves, is that, under some conditions, the braid type of a
set of one-periodic orbits of a Hamiltonian diffeomorphism on a surface
is stable under perturbations that are sufficiently
small with respect to Hofer's metric. As a consequence one obtains that
the topological entropy is lower semi-continuous on the group of
Hamiltonian diffeomorphisms on a closed surface, as well on the group of
compactly supported Hamiltonian diffeomorphisms
on the two-dimensional disc. This talk is based on joint works with
Arnon Chor, and Marcelo Alves.
14:00 Erman Cineli (Jussieu)
Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective.
Abstract: In this talk I will introduce barcode entropy and discuss its connections to topological entropy. The barcode entropy is a Floer-theoretic invariant of a compactly supported Hamiltonian diffeomorphism, measuring, roughly speaking, the exponential growth under iterations of the number of not-too-short bars in the barcode of the Floer complex. The topological entropy bounds from above the barcode entropy and, conversely, the barcode entropy is bounded from below by the topological entropy of any hyperbolic locally maximal invariant set. As a consequence, the two quantities are equal for Hamiltonian diffeomorphisms of closed surfaces. The talk is based on a joint work with Viktor Ginzburg and Basak Gurel.
15:45 Ailsa Keating (Cambridge) - ON LINE
Symplectomorphisms of some Weinstein four-manifolds.
Abstract: Let
M be the Weinstein four-manifold mirror to Y \ D for (Y,D) a log
Calabi--Yau surface; this is usually the Milnor fibre of a cusp
singularity. We introduce two families of symplectomorphisms of M:
Lagrangian translations, which we prove are mirror to tensors with line
bundles; and nodal slide recombinations, which we prove are mirror to
automorphisms of Y. Together with spherical twists, these are expected
to generate the symplectic mapping class group of M. Time permitting,
some applications will be given. Joint work with Paul Hacking.
Prochaines séances: 4 février (M.
Bertelson, ?, ?), 11 mars (A. Gadbled, Y. Rollin, ?)
Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay (à Nantes le 10 décembre)
- Symplectic Zoominar (les vendredis hors symplectix à 15:15, heure de Paris)
