Seth Baldwin (UNC), GMA Seminar

Title: The additive eigenvalue problem and the saturated tensor problem.

Abstract:  The Hermitean eigenvalue problem, originating with the work of Weyl in 1912, is concerned with determining the possible eigenvalues of the sum of two Hermitean matrices with prescribed eigenvalues.  It was not until the work of Klyachko (1998) and Knutson-Tao (1999) that the problem was finally resolved.  Interestingly, the solution involves the identification of the problem with a problem in representation theory called the saturated tensor problem, which concerns the decomposition of the tensor product of two irreducible representations of a semisimple Lie group into irreducible factors.  In this talk I will introduce both problems, focusing on on the example of the general linear group, and explain their equivalence.  Time permitting, I will state a solution to the saturated tensor problem.

The first portion of this talk will be accessible to anyone with a background in linear algebra.  First year graduate students interested in algebra or representation theory, as well as any graduate students who have taken a course in Lie algebras or Lie groups, are encouraged to attend.