Working seminar on symplectic topology and related topics

• Nov 9: Vincent Humilière
    Title: Relation between periodic Floer homology and link Floer homology (after Guanheng Chen) I
    Abstract: Link Floer homology and Periodic Floer homology are both invariants of area preserving diffeomorphisms of surfaces that were involved in recent progress on C-infinity closing lemma and simplicity conjecture. The goal of the talk is to learn about the papers arxiv:2111.11891 and arxiv:2209.11071 by G. Chen which establishes a relation between these two theories. In the first part we will review link Floer homology, which is a Lagrangian Floer theory in d-fold symmetric products (dimension = 2d) and see that it admits an alternative definition that uses curves in a 4 dimensional manifold. This is due to Chen and inspired by Lipshitz's interpretation of Heegaard Floer theory.
• Nov 16: Vincent Humilière
    Title: Relation between periodic Floer homology and link Floer homology (after Guanheng Chen) II
• Nov 23: Francesco Morabito
    Title: Hofer Pseudonorms on Braid Groups and Quantitative Heegaard-Floer Homology
    Abstract: Given a lagrangian link with k components it is possible to define an associated Hofer pseudonorm on the braid group with k strands. In this talk we are going to detail this definition, and explain how it is possible to prove non degeneracy if k=2 and certain area conditions on the lagrangian link are met. The proof is based on the construction, using Quantitative Heegaard-Floer Homology, of a family of quasimorphisms which detect linking numbers of braids on the disk.
• Nov 30: Matija Sreckovic
    Title: Higher-Dimensional Heegaard-Floer Homology
    Abstract: The goal of my talk will be to give a survey of the paper "Applications of higher-dimensional Heegaard-Floer homology to contact topology" by V. Colin, K. Honda and Y. Tian (arxiv:2006.05701 ). In the first part of the talk, I will define the higher-dimensional Heegaard-Floer homology groups (HDHF) associated to a Weinstein domain W and a symplectomorphism h of W which restricts to the identity on the boundary.
  In the second part of the talk, I will define the contact class in HDHF and explain how it can be applied to detect non-Liouville-fillability of some contact manifolds, as well as the existence of closed Reeb orbits. If time permits, I will also say a few words about the variant of symplectic Khovanov homology defined in this paper.
• Dec 7: No seminar
• Dec 14: No seminar (the speaker caught covid...)
• Jan 18: Dustin Connery-Grigg
    Title: Understanding the geometry of Hamiltonian Floer complexes of Hamiltonian isotopies on surfaces (Part 1)
    Abstract: In arXiv:2102.11231 I explained how, for Hamiltonian isotopies on surfaces, one can use ideas originating in Hofer-Wysocki-Zehnder’s work on finite energy foliations (along with later developments due to Siefring) together with the topology of capped braids in order to gain significant insight into the topological behaviour of various collections of Floer-type cylinders which are relevant to fundamental constructions in Floer theory. Some notable applications of this theory are the provision of an explicit bridge between Floer theory and Le Calvez’s theory of transverse foliations, as well as both motivating the introduction of a novel class of spectral invariants in addition to providing a purely topological characterization of the most important of these. In these two talks, I will aim to explain the main ideas and details of this theory.
• Jan 25: Dustin Connery-Grigg
    Title: Understanding the geometry of Hamiltonian Floer complexes of Hamiltonian isotopies on surfaces (Part 2)
    Abstract: Continuation of Part 1
• Feb 1: Vukasin Stojisavljevic
    Title: An introduction to topological entropy
    Abstract: This will be an introductory talk on topological entropy. We will start from the definition, discuss basic properties of topological entropy and illustrate the relevant notions in certain classical examples. We will also briefly discuss theorems of Yomdin and Newhouse which relate topological entropy of smooth maps on compact manifolds to the volume growth of subsets. This will be the first in a series of talks on topological entropy, which aim at understanding the recent paper of Ginzburg, Gurel and Mazzucchelli - https://arxiv.org/abs/2212.00943.
• Feb 8: Erman Cineli
• Feb 15: TBA
• Feb 22: No seminar
• Mar 1: TBA
• Mar 8: Ibrahim Trifa
• Mar 15: Yusuke Kawamoto (TBC)