Dahye Cho, Yonsei University
2023 AWM Research Symposium
Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]

There is a spectral sequence converging to symplectic cohomology of an affine variety whose E1-page consists of symplectic cohomology of the complement of a hypersurface in the affine variety. We will talk about a contact (as well as S1-equivariant) version of the spectral sequence and provide applications including the invariants of fibered knots and the invariants of isolated hypersurface singularities. The data of each page of the spectral sequence consist of the invariants. If time permits, we will talk about properties of the relative contact homology and relations to other Floer-theoretic invariants.

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