Ben Webster, MIT

TITLE: Knot homology and geometry

ABSTRACT: I'll try to describe how Khovanov's HOMFLY homology for knots, while initially a bit daunting, is really a very natural construction, if one defines the HOMFLY polynomial correctly. Along the way, we'll discuss what Hecke thought the Hecke algebra was, why the structure of the flag variety is important in knot invariants, and a little bit of philosophy about why geometrizations and categorifications tend to come in pairs.