Math ColloquiumNovember 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.
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.