Floer theory of symmetric products and Hilbert schemes

Floer theory of symmetric products and Hilbert schemes

This workshop, sponsored by AIM and the NSF, 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.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

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