Séminaire Symplectique
organisé par l'équipe Géométrie
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Symplectic Zoominar: Three 20min research talks
31 janvier 2025 - 15:15Salle de séminaires IRMA
Zhen Gao (Augsburg)
Title: Morse-Bott Floer homology and rectangular pegs
Abstract: The rectangular peg problem, an extension of the square peg problem, is easy to outline but challenging to prove through elementary methods. In this talk, I discuss how to show the existence and a generic multiplicity result assuming the Jordan curve is smooth, utilizing Morse-Bott Floer homology. In particular, we obtain a convenient formula for computing the algebraic intersection number of cleanly intersecting Lagrangian submanifolds, which is well consistent with the Euler characteristic of Morse-Bott Floer homology in the spirit of ``categorification''.
Zihong Chen (MIT)
Title: The exponential type conjecture for quantum connection
Abstract: The (small) quantum connection is one of the simplest objects built out of Gromov-Witten theory, yet it gives rise to a repertoire of rich and important questions such as the Gamma conjectures and the Dubrovin conjectures. There is a very basic question one can ask about this connection: what is its formal singularity type? People's expectation for this is packaged into the so-called exponential type conjecture, and I will discuss a proof in the case of closed monotone symplectic manifolds. My approach follows a reduction mod p argument, by combining Katz's classical result on differential equations and the more recent quantum Steenrod operations.
Jonghyeon Ahn (UIUC)
Title: S^1-equivariant relative symplectic cohomology and relative symplectic capacities
Abstract: In this talk, I will construct an S^1-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, I will construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative symplectic capacities can detect the diplaceability and the heaviness of a compact subset of a symplectic manifold. We compare the first relative Gutt-Hutchings capacity and the relative symplectic (co)homology capacity and prove that they are equal to each other under a convexity assumption. -
Richard Hind
Zoominar: Lagrangian intersections and the shape invariant
14 février 2025 - 15:00Salle de séminaires IRMA
We will outline the proof of an intersection result between embedded Lagrangian tori and certain 1 parameter families of product Lagrangian tori in the 4 dimensional symplectic cylinder. The theorem can be applied to give new computations of the shape invariant, describing the Lagrangian tori in some toric domains, and therefore to produce symplectic embedding obstructions. This is joint work with Ely Kerman. -
Pierre-Alexandre Arlove
Contact non-squeezing in various closed prequantizations
21 février 2025 - 15:00Salle de séminaires IRMA
Abstract: I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations. The proof is based on the construction of contact capacities coming from spectral selectors defined on the contactomorphisms group of the latter contact manifolds. I will define all these notions during my talk.