Aleksander Doan - Equivariant transversality meets geometric measure theory

July 2, 12 pm ET: Aleksander Doan (Columbia), Equivariant transversality and curve counting

Abstract: This talk is motivated by the problem of counting embedded pseudo-holomorphic curves in symplectic manifolds. Typically, naive counting embedded curves does not lead to a symplectic invariant as they can degenerate to singular or multiply covered curves. I will discuss a result, obtained in collaboration with Thomas Walpuski, which excludes such degenerations in certain situations. The proof of this result combines Wendl's recent theorem on equivariant transversality for multiply covered curves with methods of geometric measure theory. Time permitting, I will talk about an idea of defining invariants of symplectic six-manifolds by counting embedded pseudo-holomorphic curves and solutions to gauge-theoretic equations.