Categorification of quantum group representations and its application in low-dimensional topology

Mikhail Khovanov
University of California at Davis
Mathematics

We will survey known and conjectural realizations of finite-dimensional
representations of simple Lie algebras and quantum groups as Grothendieck
groups of abelian and triangulated categories. These constructions should
lead to a lift of quantum polynomials of links to cohomology theories of links
and invariants of link cobordisms.


Back to Representation of Loop Groups