2/5 and 2/12 at 17:30 in 507

Shaoyun Bai

Title for 2/5: Infinitude of Hamiltonian periodic orbits and GLSM

Abstract: Take an irrational rotation of the two-sphere; it only has the north and south poles as its periodic points. However, Franks proved that for any area-preserving diffeomorphism of the two-sphere, if it has more than two fixed points, then it must have infinitely many periodic points. I will discuss a generalization with Guangbo Xu of this result to all compact toric manifolds, for which GLSM plays a surprising role.

Title for 2/12: Gromov-Witten invariants and complex cobordism

Abstract: GW invariants are defined from moduli spaces of stable maps, which are singular spaces but come with virtual fundamental classes. Since the beginning of this subject, it has been speculated that GW invariants should admit refinements in complex cobordism. I will discuss a resolution of this question joint with Abouzaid, building on recent advances in symplectic topology and functorial resolution of singularities.