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Khovanov homology via geometric representation theory

Colloquium

Speaker: Joel Kamnitzer, UC Berkeley
Location: 1147 MSB
Start time: Tue, Oct 2 2007, 4:10PM

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 (and Rozansky) enhanced the Jones polynomial and other RT invariants to knot homology theories. After explaining these theories, I will explain a construction (joint with Sabin Cautis) of Khovanov homology using geometric representation theory and specifically the geometric Satake correspondence.