Center for Applied Mathematical Sciences Visit USC
USC Donrsife Homepage
Mar 12
3:45 PM - 4:45 PM SAL 101
Khovanov Homology And Gauge Theory CAMS Distinguished Lecturer
Joint with the Department Colloquium
Edward Witten Institute for Advanced Study

In this talk, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and five-dimensional manifolds with boundary, with a rather subtle boundary condition that encodes the knots and links. The construction is formally analogous to Floer and Donaldson theory in three and four dimensions. It was discovered using quantum field theory arguments but can be described and understood purely in terms of classical gauge theory.

Previous colloquium: The evolution of vortices in planar flows Next colloquium: Object configuration models in computer vision