Tentative Program:

9AM-10AM (Minicourse 1)

10:30AM-11:30AM (Minicourse 2)

11:30--1:30 (Lunch)

1:30--1:55 (Short talk 1)

2:00-2:25 (Short talk 2)

2:30-2:55 (Short talk 3)

3:45-4:455(Minicourse 3)

Last Day: No short talks.

Monday: Morning: Lee, Seidel, Afternoon: Chanda

Tuesday: Morning: Lee, Seidel, Afternoon: Chanda

Wednesday: Morning: Lee, Seidel, Afternoon: Chanda

Thursday: Morning: Shelukhin, Bai/Xu, Afternoon: Shelukhin

Friday: Morning: Bai/Xu, Shelukhin, Afternoon: Bai/Xu

Short talk list: Kenny Blakey, Yonghwan Kim, Roman Krutowski, David Keren Yaar, Shuhao Li, Jiaji Cai, Samuel Sottile, Advika Rajapakse, Hanming Liu, Gabriel Beiner, Josie Hlavinka, Polyana Benk, Shanon Rubin

Short talk Title and Abstract

Gabriel Beiner 

Title: Infinite ECH Capacities and Anosov Flows

Abstract: The ECH capacities are powerful invariants for studying four-dimensional symplectic embeddings, but little is known about them beyond domains with very simple topology. I will discuss some recent work relating embedded contact homology (ECH) with the theory of Anosov flows, which allows one to show the ECH capacities are infinite for many examples. This has applications to obstructing high-genus Lagrangian embeddings. It also gives constraints on the existence of Anosov flows in various settings, in particular addressing an old question of Herman. 

David Keren Yaar

Title: Tightness of Chekanov’s bound on displacement energy for small Chekanov tori in projective space

Abstract: We compute the displacement energy of displaceable Chekanov tori in $CP^n$ and the minimal area of pseudo-holomorphic disks with boundary on them. This talk is based on my master's thesis, supervised by Leonid Polterovich, Sara Tukachinsky-Kahnonitch, and Joé Brendel.

Jiaji Cai

Title: Symplectic irrationality via Gromov-Witten theory

Abstract: Determining the rationality of varieties is a fundamental problem in algebraic geometry. By replacing complex blow-ups with Gromov's notion of symplectic blow-ups, we obtain a symplectic notion of rationality. In this talk, I will explain how Gromov-Witten theory can be used to obstruct the symplectic rationality of certain smooth projective hypersurfaces.

Samuel Sottile

Title: Almost Toric Fibrations in Higher Dimensions.

Abstract: While there is a well-understood theory of almost toric fibrations for symplectic four-manifolds, there are few non-trivial examples in higher dimensions. In this talk, I will discuss how to extend almost toric fibrations to higher dimensions, and machinery used for constructing them. In particular, I will show that many complete intersections in toric varieties with effective first Chern class admit such a fibration. For example, Batyrev-Borisov mirror pairs have dual almost toric fibrations.

Roman Krutowski

Title: On Fukaya categories of cotangent bundles of global quotient orbifolds.

Abstract: To any global quotient orbifold [X/G] associated with an effective action of a finite group G on a complex manifold X by biholomorphisms, one associates its Hecke algebra, which is a deformation of the group algebra of the orbifold fundamental group of [X/G]. 

I will explain that under some assumptions the wrapped Fukaya category of the cotangent bundle T^*[X/G] recovers the orbifold Hecke algebra, as the 0-th cohomology of the endomorphisms of a regular fiber. The crucial tool is the novel result on the censorship of orbighost bubbles. The talk reports on the joint work with Honda, Tian, and Yuan.

Shuhao Li

Title: Open-closed string topology and Lagrangian embeddings

Abstract: The Maslov class is a basic invariant of a Lagrangian submanifold. However, many fundamental questions concerning constraints on the Maslov classes of Lagrangian embeddings (known as Maslov class rigidity) remain open. For example, the existence/non-existence of a Maslov-zero Lagrangian embedding of a given closed manifold L into the standard symplectic vector space C^n is a well-known problem. I will speak about a new approach to these types of questions using a construction of a (curved) deformation of the dg algebra of chains on the based loop space, following ideas from open-closed string topology, and derive new results on the Maslov class rigidity question.

Kenny Blakey

Title: An overview of Floer homotopy

Abstract: In this talk, I would like to give an overview of Floer homotopy theory and, time permitting, its relation to various other things: bordism, spectral Gromov-Witten theory, and string topology. Some parts might be based on joint work with various collaborators: Ciprian Bonciocat, Noah Porcelli, and/or Liam Keenan.