UK WILDCATS Seminar

"Topological and combinatorial constructions in the representation theory of sl_n and S_n"

Julianna Tymoczko
University of Iowa

Monday, May 18, 2009
4:00 pm, 845 Patterson Office Tower

Abstract:

While developing what is now known as Khovanov homology, Khovanov studied a remarkable ring. It has a basis of noncrossing matchings, while its ring structure encodes both a knot theoretic invariant and the tensor product structure of sl_2 representations. Even more surprisingly, it is isomorphic to the cohomology of a particular Springer variety, a key element in a geometric construction of representations of the permutation group S_n.

This led to a collection of conjectures and results connecting the geometry of Springer varieties to sl_n representations through topological and combinatorial constructions, which we will discuss. We will not assume any particular background knowledge, except linear algebra.