**Special Seminar**

Come join us on **Friday, January 20, 2023 at 10:30am in room 520, Professor Kyle Hayden** (Rutgers University-Newark) will be giving a special lecture titled “**Surfaces and 4-manifolds**” (Moreā¦).

**Abstract**: The topology of smooth manifolds is governed largely by geometry in low dimensions and by algebraic topology in high dimensions. The phase transition occurs in dimension four, where continuous and differential topology split apart and “exotic” phenomena emerges. I will begin by describing how this phase transition can be studied via embedded surfaces in4-manifolds, then I will survey recent developments in this area. In particular, I will explain how quantum invariants (such as Khovanov homology)have recently been used to address existence and uniqueness questions about surfaces in 4-manifolds — and what this might imply for foundational questions about 4-manifolds themselves.

**Location**: Mathematics Hall, room 520

**Date**: Friday, January 20, 2023 at 10:30am