### Monday September 20, 2004

**Speaker**: Harry Tamvakis

**Title**: Schubert Calculus and Lie Group Representations

**Abstract**: Suppose that *G* is a Lie group and *P* a
parabolic subgroup of *G*. The multiplicative structure of the
cohomology ring of the homogeneous space *X=G/P* is known as
"Schubert calculus", after the classical theory in the case when *X*
is a type A Grassmannian. Is the Schubert calculus for
*H*(X)* somehow related to the structure of the
representation ring of *G* (where the product is given by the
product of characters of *G*)? I will discuss some old and recent
results which give insight on the answer.