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 Julian Chaidez (Princeton)
Legendrian ECH.
Abstract: Embedded contact homology (ECH) is a flavor of SFT for contact 3-manifolds that has been very successful at resolving open problems in Reeb dynamics, such as the Weinstein conjecture. Many versions of SFT admit generalizations to relative theories involving Legendrian (or Lagrangian) boundary conditions. The goal of this talk will be to explain the construction of the Legendrian version of ECH and discuss various potential applications and open problems. Our construction builds on several ideas present in previous works, such as Colin-Ghiggini-Honda's isomorphism between HF and ECH. This is joint work with Oliver Edtmair, Luya Wang, Yuan Yao and Ziwen Zhao.
14:00 Thomas Massoni (Princeton)
Anosov flows, non-Weinstein Liouville domains and their wrapped Fukaya categories.
Abstract: While Weinstein domains and their symplectic invariants have been extensively studied over the last 30 years, little is known about non-Weinstein Liouville domains. We present a construction in dimension four based on Anosov flows on three-manifolds. The symplectic invariants of these ``Anosov Liouville domains'' constitute new invariants of Anosov flows. The algebraic structure of their wrapped Fukaya categories is in stark contrast with the Weinstein case. We focus on a subcategory $\mathcal{W}_0$ of the wrapped Fukaya category whose objects are in bijection with the simple closed orbits of the flow. Surprisingly, $\mathcal{W}_0$ is not homologically smooth, as it is not finitely split-generated in a maximal way. This talk is mostly based on joint work arXiv:2211.07453 with Kai Cieliebak, Oleg Lazarev and Agustin Moreno.
15:45 Oliver Edtmair (Berkeley)
Disk-like surfaces of section and symplectic embeddings.
Abstract: Symplectic embedding problems, i.e. the question whether one symplectic manifold embeds into another, are of central importance in symplectic geometry. Such problems are intimately related to Hamiltonian dynamics and this relationship has been used to construct a plethora of obstructions to symplectic embeddings. Going in the opposite direction, I will discuss how disk-like global surfaces of section, a concept from dynamics, can be used to construct symplectic embeddings. This yields partial progress towards Viterbo’s conjecture on symplectic capacities of convex domains: In dimension four, the cylindrical embedding capacity agrees with the minimal action of an unknotted Reeb orbit.
Next Symplectix:
Feb 3 (Bottman, Smith, Mazzucchelli), Mar 6 (Theillere, ?, ?)...
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
