This talk is based on a beautiful result due to Knutson and Tao: https://www.ams.org/notices/200102/fea-knutson.pdf, which discusses the following question: Given two hermitian matrices $A, B$, and how can the eigenvalues of $A+B$ be bounded by that of $A$ and that of $B$? The problem was expressed more explicitly by Weyl and Horn via a series of inequalities, which was conjectured to have exhausted the relations. Knutson and Tao later found out this can be expressed using some interesting geometric structure like honeycomb.