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)

3:45-4:45(Minicourse 3)

Last Day: No short talks and Minicourse 3 will be moved to 1:30PM.

Monday: Morning: Lee, Seidel, Afternoon: Chanda

Tuesday: Morning: Lee, Seidel, Afternoon: Chanda

Wednesday: Morning: Lee, Seidel, Afternoon: Chanda (3:00 - 4:00)

Thursday: Morning: Shelukhin, Bai, Afternoon: Shelukhin

Friday: Morning: Bai, Shelukhin, Afternoon: Bai

Short talk Title and Abstract

Monday

Yonghwan Kim

Title: Circle-valued Morse theory in positive characteristic

Abstract: We define an analogue of Hutchings-Lee's torsion invariant for circle-valued Morse functions in positive characteristic. We study phenomena that arise from specializations at roots of unity in finite characteristic, and how the corresponding information is distributed among Morse trajectories and closed gradient orbits.

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. 

Shanon Rubin

Title: A homotopical invariant of Weinstein surfaces  

Abstract: Following Nadler's program, it is expected that given a Weinstein manifold with arboreal skeleton, one should obtain its Kashiwara-Schapira stack by gluing together the microlocal sheaf categories at each arboreal singularity. In this talk, I will describe explicit models for the homotopy limits of diagrams of such dg-categories arising from Weinstein surfaces. This is done by characterizing all relevant Reedy model structures on the categories of diagrams that arise. After modifying with appropriately chosen shifts, invariance under Weinstein homotopies follows using a complete set of moves of arboreal skeleta in dimension 2.

Tuesday

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.

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.

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.

Wednesday

Advika Rajapakse

Title: A classification of some cohomology operations for Khovanov homology.

Abstract: Using the ideas of Floer homology and Floer homotopy, Lipshitz-Sarkar constructed a space-level link invariant arising from Khovanov homology. That is, for each link L in S^3, they assign a stable homotopy type X(L). Such invariants show the existence of cohomology operations, called Steenrod squares, on Khovanov homology, although explicit computation is a technical challenge. Later, Morán introduced combinatorially defined cohomology operations sq^n on Khovanov homology, although their connection to Steenrod squares has remained largely open. In this talk, we prove that the cohomology operations sq^2, sq^3 are Steenrod squares, and prove the relation sq^1 sq^{2n} = sq^{2n+1}.

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 the 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.

Josephine Hlavinka

Title: Homological Mirror Symmetry for Acyclic Cluster Varieties

Abstract: We prove homological mirror symmetry for acyclic cluster varieties.

Thursday

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.

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.

Polyana Benk

Title: Caustics of Lagrangians and Stably Trivial Lagrangian Distributions

Abstract: Let (M^{2n},\omega) be a symplectic manifold, (\gamma\subset TM) a Lagrangian distribution, and (L\subset M) a closed Lagrangian submanifold. We study the problem of realizing (L) with only fold-type tangencies to (\gamma). An (h)-principle reduces this geometric problem to a homotopy problem for Lagrangian distributions: if (\gamma) is homotopic to a Lagrangian distribution with respect to which (L) has only fold-type tangencies, then (L) can be Hamiltonian isotoped to achieve this property for (\gamma). We introduce formal folds and the first Maslov class, and show that the existence of fold-type tangencies together with a trivial first Maslov class implies that the Lagrangian distribution is stably trivial. We then formulate a conjecture concerning the existence of a homotopy to a Lagrangian distribution with only fold-type tangencies.