The University of Michigan


Abstract 

The SchurHorn theorem characterizes eigenvalues and diagonal entries of Hermitian matrices. The Horn problem characterizes eigenvalues of sums of Hermitian matrices. There are similar results for singular values of sums and products of arbitrary matrices. After summarizing recent work on these problems, we will discuss some variations, including the problem of characterizing invariants of offdiagonal blocks in terms of invariants of the whole matrix. The solutions involve the geometry of Schubert calculus as well as some combinatorics involving LittlewoodRichardson coefficients. Large part of the talk will be based on the recent paper by S.F., W.F., ChiKwong Li, and YiuTung Poon.
(The speakers will speak sequentially rather than
simultaneously.)
