© | << < ? > >> | Dror Bar-Natan: Talks:

Expansions and Quantum Groups

Brown University, November 14, 2007

Abstract. I don't understand quantum groups. My talk will be about my struggle to understand them as "expansions". So I will start with the definition of an expansion (an isomorphism of the unipotent completion of a group or another algebraic object with its associated graded space). I will explain how expansions may be useful (they are about "polynomial functions" on anything, and they allow for iterative investigation of "definable properties"). I will give a couple of examples (free groups, braids, knotted trivalent graphs). Finally I will tell you why I think the coolest explanation of quantum groups (deformations of universal enveloping algebras) ought to be given using expansions of virtual knots.

If you don't know what quantum groups are, you'll come out of my talk still not knowing. If I don't understand quantum groups, neither shall you. But you will appreciate expansions.

"God created the knots, all else in topology is the work of mortals."

Leopold Kronecker (modified)