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SUMMARY:Fixed point Floer cohomology and the enumerative geometry of singu
 lar hypersurfaces - Maxim Jeffs (Cambridge)
DTSTART:20241204T160000Z
DTEND:20241204T170000Z
UID:TALK220942@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:I'll explain how\, for singular hypersurfaces\, a version of t
 heir genus-zero Gromov-Witten theory may be described in terms of a direct
  limit of fixed point Floer cohomology groups. This construction is easy t
 o define and very amenable to computation. As an illustration\, I'll talk 
 about joint work with Yuan Yao and Ziwen Zhao\, where we calculate the ful
 l 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≥1 contain no non-constant 
 rational curves\, these types of enumerative invariants are not possible t
 o obtain using classical curve-counting methods. To finish\, I'll discuss 
 our ongoing project studying enumerative geometry and mirror symmetry for 
 mirror pairs of singular K3 surfaces.
LOCATION:MR13
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