Kyle Hayden (Columbia University)

Title: Exotic ribbon disks and symplectic surfaces

Abstract: One approach to understanding the smooth topology of a 4-dimensional
manifold is to study the embedded surfaces it contains. I'll construct
new examples of "exotically knotted" surfaces in 4-manifolds,
i.e. surfaces that are isotopic through ambient homeomorphisms but not
through diffeomorphisms. We'll begin with simple examples of exotic
disks in the 4-ball. Then we'll turn to the symplectic setting and
exhibit new types of exotic phenomena among symplectic, holomorphic,
and Lagrangian surfaces.