|TITLE:||Categorification of quantum groups|
|SPEAKER:||Mikhail Khovanov (Columbia University)|
|DATE:||Vendredi, 23 Avril 2010|
To an algebra A there is associated the Grothendieck group K_0(A) generated by symbols of projective modules over A. In certain cases K_0(A) can be made into a ring. In this talk, we'll construct an algebra with the Grothendieck group naturally isomorphic to an integral form of the quantized universal enveloping algebra of a simple Lie algebra (an integral version of the so-called "quantum group"). The algebra has a diagrammatical description, with elements given by braid-like planar pictures and strands labelled by simple roots of the Lie algebra.
About the speaker: Mikhail Khovanov received his Ph.D. from Yale University in 1997. He then spent two years at the Institute of Advanced Study before becoming an assistant and then associate professor at the University of California, Davis. He has been a full professor at Columbia University since 2007. His research interests include knot theory, algebraic topology, and Lie theory. He is most well known for developing what is now known as the Khovanov homology for links, introduced in his seminal paper "A categorification of the Jones polynomial." This was one of first examples of a "categorifcation" and has spawned new directions of research in knot and Lie theory.