# Math Colloquium

*November 29, 2010*

The last Math Colloquium of the semester will be **Tuesday, November 30** at **3:30 p.m. in VH1228**. **Calin Chindris** of the University of Missouri will be speaking on **Eigenvalues of Sums of Hermitian Matrices**. After the talk he will be able to answer questions on graduate study at Mizzou. As usual, refreshments will be provided.

ABSTRACT

In 1912, H. Weyl asked for a description of the eigenvalues of a sum of two

Hermitian matrices in terms of the eigenvalues of the summands. In 1962, A. Horn recursively constructed a list of inequalities for the eigenvalues of two

Hermitian matrices and their sum, which he conjectured to be necessary and sufficient. In 2000, Horn’s conjecture was finally proved. In this talk, I will describe the Horn’s eigenvalue inequalities, and explain how the Weyl’s eigenvalue problem relates to other problems, including the

existence of short exact sequences of finite abelian p-groups and the non-vanishing of the Littlewood-Richardson coefficients.