3:00 p.m., Wednesday (January 24, 2007)
A geometric representation theory approach to Khovanov's knot homology
The Jones polynomial is a powerful polynomial knot invariant which
was discovered in the early 1980s. In the late 1980s, Reshetikhin-Turaev showed that the Jones polynomial fits into a family of knot invariants coming from representation theory. Recently, Khovanov
enhanced the Jones polynomial to a homology theory. After explaining
these theories, I will explain a construction (joint with Sabin
Cautis) of Khovanov homology using derived categories of coherent
sheaves on certain varieties arising in the geometric Langlands program.
Refreshments will be served at 2:45 p.m. (PIMS Lounge).