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Symplectic Geometry Seminar

Fixed point Floer cohomology and the enumerative geometry of nodal curves (Maxim Jeffs)

Maxim Jeffs (Simons Center for Geometry and Physics)

Location:  Hill 705
Date & time: Thursday, 22 February 2024 at 1:30PM - 2:30PM

Abstract: I'll explain how, for singular hypersurfaces, a version of their genus-zero Gromov–Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups. This construction is easy to define and very amenable to computation. As an illustration, I'll talk about recent joint work with Yuan Yao and Ziwen Zhao, where we calculate the full ring structure on this direct limit in the case of Dehn twists on curves, giving a direct proof of closed-string mirror symmetry for nodal curves. These calculations involve contributions from counts of many non-trivial holomorphic curves; since curves of genus (g geq 1) contain no non-constant rational curves, these types of enumerative invariants are impossible to obtain using classical curve-counting methods. To finish, I'll discuss our ongoing project studying enumerative geometry and mirror symmetry for singular varieties using fixed point Floer cohomology.