Location: IHP, room 201
The seminar will take place in presence, but will be broadcasted via zoom:
https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Luca Asselle (Bochum)
Morse homology for the Hamiltonian action in cotangent bundles
Abstract: As first shown by Viterbo in a seminal paper from 1999, Floer homology for the
Hamiltonian action functional for closed loops in the cotangent bundle of a closed smooth manifold
is well-defined and in an essentially canonical way isomorphic to the loop space homology
(in case of spin manifolds), provided the Hamiltonian is asymptotically quadratic in the fibre.
In this talk I will show that, for such Hamiltonian actions, Morse homology is indeed well-defined
in a direct way. The key idea is that the fibrewise linear structure of the cotangent bundle allows
to split the Sobolev space setup for the loop space (according to the polarisation
of the cotangent bundle as a family of Lagrangian fibres) such that the resulting Hilbert manifold
of loops provides the Palais-Smale property for the action functional. The construction of Morse
homology is then completed following the abstract work of Abbondandolo and Majer. As one expects,
the resulting Morse homology is isomorphic to Floer homology. However, the Morse homology approach
has potentially several advantages which will be discussed if time permits.
14:00 Denis Auroux (Harvard)
Fukaya categories of Landau-Ginzburg models and functoriality in mirror symmetry.
Abstract: The central topic of this talk will be Fukaya categories of Landau-Ginzburg models (i.e., symplectic fibrations over the complex plane). We will describe several natural functors relating these to other flavors of Fukaya categories, and the interpretation of these functors under mirror symmetry, where they correspond to inclusion and restriction functors between derived categories of coherent sheaves on a variety and a hypersurface inside it. The talk will be mostly
expository; the non-expository parts are joint work with Mohammed Abouzaid on one hand, and the thesis work of Maxim Jeffs on the other hand.
15:45 Yuichi Ike (Tokyo)
Completeness of interleaving distance on Tamarkin category and C^0-symplectic geometry.
Abstract: The Tamarkin category is a sheaf category that can be used for studying non-displaceability problems in symplectic geometry. One can equip the category with a canonical interleaving-like distance to get quantitative information on Hamiltonian diffeomorphisms. In particular, the distance is stable with respect to Hamiltonian deformations of sheaves, which gives a sheaf-theoretic lower bound of displacement energy. In this talk, I will explain the completeness of the distance and its application to C^0-symplectic geometry. For that purpose, we also develop the Lusternik--Schnirelmann theory for sheaves. Joint work with Tomohiro Asano.
Next Symplectix:
Nov 18, Dec 2, Jan 6 ...
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
