Leicester Pure Mathematics Seminar, 05/11/2009
Thurs 4pm, MAB 119
Geordie Williamson (University of Oxford): Knot homology and geometric representation theory
I will start by describing Khovanov's idea of "knot homology". The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using techniques from geometric representation theory. This leads to some interesting links between knot theory and Hecke algebras, braid groups and finite groups of Lie type.