Gauge Theory and Khovanov Homology

Speaker: Edward Witten

Date: Sat, Feb 18, 2012

Location: PIMS, University of Washington

Subject: Mathematics, Differential Geometry and Geometric Analysis, Topology, Physics, Mathematical Physics, Particle Physics and Quantum Field Theory

Class: Scientific


After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.