Location: IHP, room 201
The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 François Loeser (Jussieu)
Arc spaces and Floer cohomology.
Abstract: Our aim is to present an intriguing connection between arc spaces as occuring in motivic integration and symplectic disks arising in Floer homology. We will mostly focus on the situation of the monodromy acting on the Milnor fiber of a complex hypersurface singularity. In this setting, the connection was upgraded recently from a relation between Euler characters to the entire cohomology. If times allows we will mention some other occurrences of this analogy..
14:00 Pierre-Alexandre Arlove (Bochum)
Contact orderability and spectral selectors.
Abstract: Some contactomorphisms groups and isotopy classes of Legendrians admit a natural partial order first studied by Eliashberg and Polterovich. In this talk I will use this partial order to define functions on the latter spaces analogous to the spectral invariants in Symplectic Geometry coming from Lagrangian Floer homology. For Legendrians, I will show that these functions are spectral selectors and, from there, derive dynamical applications concerning existence of Reeb chords and translated points. After discussing the non-degeneracy of the selectors, I will present applications to the geometric study of these spaces, namely : construction of time-functions and the study of various metrics. This is a joint work with Simon Allais.
15:45 Ipsita Datta (Zurich)
Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants.
Abstract: We introduce new invariants to the existence of Lagrangian cobordisms in R^4. These are obtained by studying holomorphic disks with corners on Lagrangian tangles, which are Lagrangian cobordisms with flat, immersed boundaries.
We develop appropriate sign conventions and results to characterize boundary points of 1-dimensional moduli spaces with boundaries on Lagrangian tangles.
Time permitting, we use these to define algebraic structures on a
related "linear" case of Lagrangian cobordisms in surface times complex plane.
This talk is based on my thesis work under the supervision of Y. Eliashberg and on work in progress joint with J. Sabloff.
Next Symplectix:
12/01 (F. Gironella, P. Chakravarthy, ?), 02/02 (M. Damian, ?, ?), 01/03 (?, ?, ?)
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
