Discrete CATS Seminar
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U N I V E R S I T Y O F K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2008 - 2009

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UK
WILDCATS
Seminar

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

Julianna Tymoczko

University of Iowa

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Monday, May 18, 2009

4:00 pm, 845 Patterson Office Tower

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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.