Subscribe to Events

Title: Steenrod operations, operads, and Lagrangian realization

Abstract: It is classically known that the fundamental class of an algebraic cycle in a smooth projective complex variety has vanishing odd Steenrod powers; this leads to the first counterexample to the integral Hodge conjecture by Atiyah and Hirzebruch. Motivated by mirror symmetry, one may ask what obstructions are there for a middle homology class of a closed symplectic manifold to be realized by a rigid Lagrangian (i.e. supporting an object of the Fukaya category). In this talk, I would like to share some ongoing (and far from complete) attempts at this question that see interesting links to Fukaya category, E_2 operadic structures, and equivariant operations in Gromov-Witten theory.