#
Floer theory of symmetric products and Hilbert schemes

December 5 to December 9, 2022
at the

American Institute of Mathematics,
San Jose, California

organized by

Mohammed Abouzaid,
Kristen Hendricks,
Robert Lipshitz,
and Cheuk Yu Mak

## Original Announcement

This workshop will be devoted to recent
developments in the study of Lagrangian Floer theory of symmetric
products of Riemann surfaces and Hilbert schemes of symplectic
4-manifolds, and their applications both to symplectic topology and the
low dimensional topology. The main topics for the workshop are:

- Finding a rigorous mathematical foundation for Aganagic's
formulation of Khovanov homology https://arxiv.org/abs/2105.06039
in terms of holomorphic curves in the symmetric product of a
surface, and perhaps connecting that formulation or her proposed
representation-theoretic construction of Khovanov homology to other
constructions (due to Cautis-Kamnitzer or Seidel-Smith), or to Heegaard
Floer homology.
- Leveraging the recent developments in
symplectic topology arising from Floer theory in symmetric products of
Riemann surfaces https://arxiv.org/abs/2105.11026
and https://arxiv.org/abs/2102.06118
to build connections between Heegaard Floer theory and symplectic
topology. We hope in particular that the computational methods developed
in Heegaard Floer theory can shed light on new problems in symplectic
topology.

## Material from the workshop

A list of participants.
A report on the workshop activities.

A list of open problems.