Symplectix 26 avril 2024

Location: IHP, room 314

The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

 
10:45 Laurent Côté (Bonn)  
Morse-Bott methods in Floer homotopy theory.
Abstract: I will talk about a joint project with Y. Baris Kartal whose purpose is to incorporate Morse--Bott methods into Floer homotopy theory. Morse--Bott methods have the prospect of being useful for two reasons. First, they simplify equivariant constructions: for example, we used these methods to define a lift of circle equivariant symplectic homology to equivariant spectra.  Second, they enable new computations. As a step in this direction, we used Morse--Bott methods to compute the (equivariant) local Floer homology of the orbit of an autonomous Hamiltonian, but I hope and expect that one can push such computations significantly further.
 

14:00 Georgios Dimitroglou Rizell (Upsala)
Non-shrinking of Legendrians in prequantization bundles and non-squeezing of open subsets.
Abstract: We use a version of Rabinowitz-Floer homology for Legendrians defined using Symplectic Field Theory, and its filtered invariance, to show that Legendrian lifts of Bohr—Sommerfeld Lagrangians cannot be ``shrunk’’ by Legendrian isotopy. Applications includes contact non-squeezing results for preimages of symplectic balls and cubes under the prequantization-bundle projection. This is joint work in progress with M. Sullivan.

15:45 Abigail Ward (Cambridge)
TBA.
Abstract: TBA.

Other symplectic activity in Paris:

- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)

Symplectix 5 avril 2024

Location: IHP, room 201

The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

 
10:45 David Bechara Senior (Aachen) 
The asymptotic action of area preserving disk maps and some of its properties.
Abstract: Given a diffeomorphism of the disk that preserves the standard symplectic form, I will introduce the asymptotic action associated to this map. I will then show a pointwise formula relating the asymptotic action to the asymptotic winding number of pairs of points. As a corollary one obtains a generalization for a well known result by A. Fathi which gives a formula for the Calabi invariant of a disk map in terms of its mean winding numbers. Additionally I will focus on how this formula can be used to study symplectic dynamical information for irrational pseudo-rotations of the disk. This talk includes joint work with Patrice Le Calvez and Abror Pirnapasov.
 

14:00 Yanki Lekili (London)
New orders associated with terminal threefold singularities.
Abstract: This is based on joint work with Jenia Tevelev. I will tell you a story of a vector bundle due to Kawamata that captures the "categorical essence" of certain terminal 3-fold singularities. Our computations are done in the mirror via Floer theory but it teaches us (with a proof!) something new about derived categories of terminal threefold singularities and noncommutative algebra by providing explicit deformations of the so-called Kalck-Karmazyn algebra associated with cyclic quotient surface singularities.

15:45 Salammbo Connolly (Orsay)
On torsion in (bi)linearized Legendrian contact homology.
Abstract: Given a Legendrian submanifold in a contact manifold, one can define its Legendrian Contact Homology (LCH). This invariant is unfortunately difficult to compute. However, there exist two more computable variants, linearized LCH (defined by Chekanov), and bi-linearized LCH (defined by Bourgeois and Chantraine). For legendrian knots in R^3, very little is known about the possibility of having torsion in these invariants when they are defined over integer coefficients. In joint work with Frédéric Bourgeois, we give properties of torsion that can appear in linearized LCH with integer coefficients, and also give the full geography of bi-linearized LCH with integer coefficients.

Next Symplectix:
 

26/04 (Coté, Ward, Dimitroglou-Rizell)

Other symplectic activity in Paris:

- Mini-course of Shaoyun Bai in the week 11/03-14/03
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)

Mini-cours Shaoyun Bai

Lectures on recent developments in Hamiltonian Floer homology

     by Shaoyun Bai (Columbia university)

Abstract: This lecture series will provide an introduction to recent conceptual and technical advances in Hamiltonian Floer theory.

 

Lecture one (Lundi 11 de 10h00 à 11h30, à Jussieu 15-16-413): In the first lecture, we will discuss how to organize moduli spaces from Floer theory into structures like flow categories (gradient flow lines), flow bimodules (continuation maps), and flow multi-modules (algebraic structures). Then, we will indicate how coherent Kuranishi-type structures can be defined and why they are relevant to defining virtual counts.

Lecture two (Mercredi 13 de 14h30 à 16h00, à jussieu 15-25-502): In the second lecture, we will focus on explaining the construction of global Kuranishi charts of various types of moduli spaces arising in Hamiltonian Floer theory.

Lecture three (jeudi 14 de 15h30 à 17h, à Orsay, salle 2L8): In the final lecture, we will introduce a perturbation scheme, known as the Fukaya-Ono-Parker perturbations, which allows one to define Hamiltonian Floer theory with integer coefficients. The principle will be sketched, emphasizing how to use this theory as a black box.