|Date||Aug 29, 2022|
This talk is intended to be a review of Seidel's 2002 ICM talk "Fukaya Categories and Deformations", from the viewpoint of symplectic cohomology. Given an affine variety, one can consider its normal crossings divisor compactification to view it as a Liouville domain: then it is believed that the differentials in symplectic cohomology should be related to relative Gromov-Witten invariants. Extrapolating this viewpoint, Borman-Sheridan-Varolgunes has conjectured that quantum cohomology can be viewed as a deformation of the "L-infinity structure" on symplectic cohomology. Though the existence of a L-infinity structure has not been proven yet, works of Tonkonog and Ganatra-Pomerleano have verified the Borman-Sheridan class for some cases.
In this talk, I will give an overview of these developments, and introduce some key properties that govern the behavior of holomorphic curves.
(Lunch: 13:00 - 14:00, Break: 15:20 - 15:30)