### Bridge trisections and minimal genus

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 25, 2019 - 14:00 for 2 hours
- Location
- Skiles 006
- Speaker
- Peter Lambert-Cole – Georgia Insitute of Technology

The classical degree-genus formula computes the genus
of a nonsingular algebraic curve in the complex projective plane.
The well-known Thom conjecture posits that this is a lower bound
on the genus of smoothly embedded, oriented and connected surface
in CP^2.
The conjecture was first proved twenty-five years ago by
Kronheimer and Mrowka, using Seiberg-Witten invariants. In this
talk, we will describe a new proof of the conjecture that combines
contact geometry with the novel theory of bridge trisections of
knotted surfaces. Notably, the proof completely avoids any gauge
theory or pseudoholomorphic curve techniques.