- This event has passed.

# Special Colloquium – Dr. Hannah Schwartz

## December 8, 2022 @ 4:00 pm - 5:00 pm

Speaker: Dr. Hannah Schwartz

Time: 4:00p-5:00p

Mode: In Person

Location: Phillips 332

Title: *A trip to the movies, starring: spheres in 4-manifolds*

Abstract: How, and why, should surfaces in 4-manifolds be visualized? We will begin by illustrating movies of knotted surfaces in four dimensions, followed by a discussion on the relevance of these pictures to the study of smooth 4-manifolds. In particular, we will examine surgery operations on smoothly embedded spheres that relate exotic pairs of smooth 4-manifolds, i.e. those that are homeomorphic but not diffeomorphic. This will provide both context and motivation for an outline of the recent “4D Light Bulb” theorems of Gabai and Schneiderman-Teichner (for spheres) along with Kosanovic-Teichner and myself (for properly embedded disks). This family of results provides conditions under which homotopy implies isotopy for surfaces in 4-manifolds.

**There will also be a Tea at 3:30pm in PH 330 with Dr. Schwartz on 12/8**.