GT seminar: The symplectic topology of contractible affine surfaces of log Kodaira dimension one

Abstract: Eliashberg's regular Lagrangian conjecture, if ture, would imply the homological essentiality of closed exact Lagrangian submanifolds in Weinstein manifolds. However, the progress towards this conjecture is very little. One instance of such an embrassment is that C^2 is the only known contractible affine surface which does not contain an exact Lagrangian surface at this point. In this talk, I will sketch a proof of the nonexistence of closed exact Lagrangian surfaces in contractible affine surfaces of log Kodaira dimension 1. The proof is based on three ingredients: Seidel representation of the fundamental group of Liouville automorphisms, McLean's technique for the symplectic cohomology of Kaliman modifications and Ganatra-Pomerleano's logarithmic PSS map.

This is a talk in our Geometry and Topology Seminar Series.