Location: IHP, room 201
The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Pierre Berger (Jussieu)
An AbC principle for pseudo-rotations.
Abstract:
We construct analytic surface symplectomorphisms with unstable elliptic
fixed points; this solves a problem of Birkhoff (1927). More precisely,
we construct analytic symplectomorphisms of the sphere and of the disk
which are transitive, with respectively only 2 and 1 periodic points.
This solves problems of proposed by Herman (1998), Fayad-Katok (2004)
and Fayad-Krikorian (2018).
To establish these results, we introduce a
principle that enables to realize, by an analytic symplectomorphism,
properties which are C⁰-realizable by the approximation by the conjugacy
method of Anosov-Katok.
14:00 Rémi Leclercq (Orsay)
Essential loops of Hamiltonian homeomorphisms.
Abstract: In 1987, Gromov and Eliashberg showed that if a sequence of diffeomorphisms preserving a symplectic form C⁰ converges to a diffeomorphism, the limit also preserves the symplectic form, even though this is a C¹ condition. This result gave rise to the notion of symplectic homeomorphisms, i.e. elements of the C⁰-closure of the group of symplectomorphisms in that of homeomorphisms, and started the study of "continuous symplectic geometry".
In this talk, I will present recent progress in understanding the fundamental group of the C⁰-closure of the group of Hamiltonian diffeomorphisms in that of homeomorphisms. More precisely, I will explain a sufficient condition which ensures that certain essential loops of Hamiltonian diffeomorphisms remain essential when seen as "Hamiltonian homeomorphisms". I will illustrate this method (and its limits) on toric manifolds, namely complex projective spaces, rational products of 2-spheres, and rational 1-point blow-ups of CP².
Our condition is based on (explicit) computation of the spectral norm of loops of Hamiltonian diffeomorphisms which is of independent interest. For example, in the case of 1-point blow-ups of CP², I will explain a surprising behavior of the spectral norm which heavily depends on the choice of the symplectic form. This is joint work with Vincent Humilière and Alexandre Jannaud..
15:45 Yash Deshmukh (Bonn)
Algebraic structures on relative symplectic cohomology.
Abstract: Abouzaid--Groman--Varolgunes constructed a chain-level framed
E2 structure on relative symplectic cohomology. In this talk, I will
outline an extension of this structure to operations parameterized by
curves of all genera and with multiple inputs and outputs. Additionally,
I will discuss the extension of this structure to include operations
from nodal curves satisfying the so-called 'plumber's condition'. I will
indicate how, in different contexts, this structure turns out to be
related to Gromov-Witten CohFTs and the graded Frobenius algebra
structure on Rabinowitz Floer theory.
Next Symplectix:
05/04 (Bechara, Lekili, Connolly), 26/04 (Coté, Ward, ?)
Other symplectic activity in Paris:
- Mini-course of Shaoyun Bai in the week 11/03-14/03
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
