Monday, October 26th, 2026
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Egor Shelukhin - Steenrod powers and Hamiltonian maps
Time: 12:30 PM - 1:55 PM
Location: Math P-131
Speaker: Egor Shelukhin
Abstract: I will report on joint work with Shaoyun Bai, Nicholas Wilkins, and Guangbo Xu, obtaining a number of definitive results in Hamiltonian dynamics on arbitrary symplectic manifolds. We rely on characteristic p methods in Floer theory including quantum deformations of Steenrod powers, first suggested by Fukaya, as well as Smith theory in Floer cohomology via the equivariant pants product introduced by Seidel. In particular, we show that, in complete generality, the existence of a symplectically degenerate maximum for a Hamiltonian diffeomorphism implies the existence of infinitely many simple periodic points, resolving an open question arising from the work of Ginzburg and Gürel.
Speaker: Egor Shelukhin
Abstract: I will report on joint work with Shaoyun Bai, Nicholas Wilkins, and Guangbo Xu, obtaining a number of definitive results in Hamiltonian dynamics on arbitrary symplectic manifolds. We rely on characteristic p methods in Floer theory including quantum deformations of Steenrod powers, first suggested by Fukaya, as well as Smith theory in Floer cohomology via the equivariant pants product introduced by Seidel. In particular, we show that, in complete generality, the existence of a symplectically degenerate maximum for a Hamiltonian diffeomorphism implies the existence of infinitely many simple periodic points, resolving an open question arising from the work of Ginzburg and Gürel.