Location: IHP, room 01 in the morning, amphi Darboux in the afternoon.
The seminar will take place in presence, but will be broadcasted via zoom
https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Maksim Stokic (Tel Aviv)
C⁰ contact geometry of isotropic submanifolds.
Abstract: Homeomorphism is called contact if it can be written as C^0-limit of contactomorphisms. The contact version of Eliashberg-Gromov rigidity theorem states that smooth contact homeomorphisms preserve contact structure. Submanifold L of a contact manifold (Y,\xi) is called isotropic if \xi|_{TL}=0. Isotropic submanifolds of maximal dimension are called Legendrian, otherwise we call them subcritical isotropic.
In this talk, we will try to answer whether the isotropic property is preserved by contact homeomorphisms. It is expected that subcritical isotropic submanifolds are flexible, while we expect that Legendrians are rigid. We show that subcritical isotropic curves are flexible, and we give a new proof of the rigidity of Legendrians in dimension 3. Moreover, we provide a certain type of rigidity of Legendrians in higher dimensions.
14:00 Vukasin Stojisavljevic (Jussieu)
Coarse nodal count via topological persistence
Abstract: Given an eigenfunction of the Laplace-Beltrami operator on a closed Riemannian manifold, its nodal domains are connected components of the complement of its zero set. A version of Courant's nodal domain theorem states that the number of nodal domains can be bounded from above in terms of the corresponding eigenvalue. A well-known question in spectral geometry asks whether a similar statement holds for linear combinations of eigenfunctions. While a direct generalization in this direction fails to be true, a positive answer can be given for coarse nodal count, i.e. by ignoring small oscillations. The proof relies on the theory of persistence modules and barcodes combined with multiscale polynomial approximations. The aim of the talk is to explain this set of ideas, how they relate to the above mentioned question, as well as how they can be used to prove other coarse extensions of the Courant's nodal domain theorem. The talk is based on a joint work in progress with L. Buhovsky, J. Payette, I. Polterovich, L. Polterovich and E. Shelukhin. 15:45 Alex Takeda (IHES) CANCELLED !
Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay (à Orsay le 18 mars)- Symplectic Zoominar (les vendredis hors symplectix à 15:15, heure de Paris)
