Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Jae Hee Lee (Stanford University) : Quantum Steenrod Operations, p-curvature, and Representation Theory

Quantum Steenrod operations are deformations of classical Steenrod operations on mod p cohomology defined by counts of genus 0 holomorphic curves with a p-fold symmetry, for a prime p. We explain their relationship with the p-curvature of the quantum connection, and survey recent developments. This relationship was first noticed through the study of quantum Steenrod operations of symplectic resolutions, a rich class of smooth symplectic manifolds arising from representation theory. We describe the role of quantum Steenrod operations in the 3D mirror symmetry program, which concerns a duality between such symplectic resolutions. Partly joint with Shaoyun Bai.

Simon Vialaret (Université Paris-Saclay) : Systolic Inequalities for $S^1$-invariant Contact Forms

In contact geometry, a systolic inequality aims to give a uniform upper bound on the shortest period of a periodic Reeb orbit for contact forms with fixed volume on a given manifold. This generalizes a well-studied notion in Riemannian geometry. It is known that there is no systolic inequality valid for all contact forms on any given contact manifold. In this talk, I will state a systolic inequality for contact forms that are invariant under a circle action in dimension three.

Kenneth Blakey (MIT) : Bounding Lagrangian Intersections Using Floer Homotopy Theory

I will describe a new lower bound on the number of intersection points of a Lagrangian pair, in the exact setting, using Steenrod squares on Lagrangian Floer cohomology which are defined via a Floer homotopy type.