Alternatively have a look at the program.

## [Bonn symplectic geometry seminar] Equivariant Floer homotopy via Morse-Bott theory

Floer homotopy type refines the Floer homology by associating a spectrum to an Hamiltonian, whose homology gives the Hamiltonian Floer homology. In particular, one expects the existing structures on the latter to lift as well, such as the circle actions. On the other hand, constructing a genuine circle action even in the Morse theory is problematic: one usually cannot choose Morse-Smale pairs/Floer data that is invariant under the circle action. In this talk, we show how to extend the framework of Floer homotopy theory to the Morse-Bott setting, in order to tackle this problem.

## Quasi-BPS categories for K3 surfaces

BPS invariants and cohomology are central objects in the study of (Kontsevich-Soibelman) Hall algebras or in enumerative geometry of Calabi-Yau 3-folds. In joint work with Yukinobu Toda, we introduce and study a categorical version of BPS cohomology for local K3 surfaces, called quasi-BPS categories. For a generic stability condition, we construct semiorthogonal decompositions of (Porta-Sala) Hall algebra of a K3 surface in products of quasi-BPS categories.

## Enumerative invariants from categories

I will talk about certain categorical invariants that are purely algebraic, Gromov–Witten-like invariants associated with smooth, proper Calabi–Yau categories. In the case of Fukaya categories, these are expected to recover the Gromov–Witten invariants of the underlying symplectic manifolds. After a brief overview of the mirror symmetry background, I will discuss an operadic interpretation of the construction of these invariants.

## Flappy trees and monoidal structures on Fukaya categories

The SYZ version of Kontsevich's Homological Mirror Symmetry conjecture predicts that if X is a symplectic manifold with the structure of a (possibly singular) Lagrangian torus fibration and with a Lagrangian section, then the split-closed derived Fukaya category should be equivalent to the bounded derived category of coherent sheaves on a "dual" fibration. The latter category has a monoidal structure coming from the tensor product, which raises a natural question: in this geometric situation, does the Fukaya category carry a monoidal structure, ideally on the chain level?

## Quantum Steenrod operations of symplectic resolutions

I will consider the quantum connection of symplectic resolutions, which is of interest in representation theory and more recently in symplectic topology. I will explain its relationship in positive characteristic with the quantum Steenrod power operations of Fukaya and Wilkins. The relationship provides a geometric understanding of the p-curvature of such connections, while also allowing new computations for quantum Steenrod operations, including the case of the Springer resolution.

## Gromov-Witten invariants via R-matrix reconstruction

Gromov-Witten theory defines a cohomological field theory (CohFT). Teleman classified semi-simple CohFTs in terms of an ‘R-matrix’. In particular, this allows one to compute higher genus Gromov-Witten invariants of spaces with semi-simple quantum cohomology from their genus 0, 3 point invariants. In this talk I will show that this approach might extend to the non semi-simple setting. The inspiration for this is the Fukaya category and the cyclic open closed map.

## Categorical dimension in microlocal geometry of cotangent bundles

We can define a Tamarkin category for an open set in a cotangent bundle using microlocal geometry of sheaves. Then it is known that the categorical dimension, which is also called the Chiu-Tamarkin invariant, of the Tamarkin category is a symplectic invariant of the open set. We will explain some geometric applications of the categorical dimension, including symplectic capacities and a Viterbo isomorphism. Part of the talk is based on a joint work with Christopher Kuo and Vivek Shende.

## Mayer-Vietoris sequence for symplectic cohomology

For a Liouville manifold and a pair of Liouville subdomains intersecting nicely, we prove a Mayer-Vietoris exact sequence relating the symplectic cohomology groups of the Liouville subdomains, their intersection and their union. This generalizes Cieliebak-Oancea's previous work on filled Liouville cobordisms. The proof uses an invariant called relative symplectic cohomology over integers. Joint work with U. Varolgunes.

## The Fukaya category of a log symplectic surface

Log symplectic structures constitute an important class of Poisson structures with well-behaved degeneracies: Since they are symplectic almost everywhere, many powerful techniques from symplectic geometry apply, but the degeneracy loci introduce local invariants.

## Floer theory and cobordism classes of exact Lagrangians

We apply recent ideas in Floer homotopy theory to some questions in symplectic topology. We show that Floer homology can detect smooth structures of certain Lagrangians, as well as using this to find restrictions on symplectic mapping class groups. This is based on joint work-in-progress with Ivan Smith.

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