Seiberg-Witten invariants

Student Geometric Functional Analysis Seminar

Meeting Details

For more information about this meeting, contact Qijun Tan.

Speaker: Damien Broka,

Abstract: Tomorrow I’ll be talking about Seiberg-Witten invariants. These are invariants cooked up from the topology of moduli spaces of solutions to the Seiberg-Witten equations. The latter are defined on compact, oriented, Riemannian, smooth four-manifolds with Spin^c(4) structure as nonlinear PDEs whose solutions are states of a very simple classical gauge field theory with much milder behavior than non-abelian Yang-Mills. The interest stems from being extra-sensitive to the differential structure, yielding invariants that sometimes allows one to distinguish different smooth structures in the same topological family. My goal tomorrow is to introduce four-dimensional spin geometry (a lot of simplifications/identifications arise which are essential to the developments of SW theory, due to quaternionic calculus being available) and study the moduli space of solutions (modded out by gauge equivalences) using the theory of elliptic PDEs and index theory. We will see it is in fact a compact, smooth, and (if time permits) a *finite dimensional* (w/ a sketch of proof) manifold! The room is 216, the time is 5pm. See you then! Best, Damien

Room Reservation Information

Room Number: 216 McAllister

Date: 10/15/2014

Time: 5:01pm - 6:01pm