Abigail Ward, MIT

Abstract: We construct a non-finite type four-dimensional Weinstein domain M_{univ} and describe a HMS-type correspondence between certain birational transformations of the complex plane preserving a standard holomorphic volume form and symplectomorphisms of M_{univ}. The space M_{univ} is universal in the sense it admits every Liouville four-manifold mirror to a log Calabi-Yau surface as a Weinstein subdomain; our construction recovers a mirror correspondence between the automorphism group of any open log Calabi-Yau surface and the symplectomorphism group of its mirror by restriction to these subdomains. This is joint work in progress with Ailsa Keating.