Abstract:

In a recent paper "The miracle of integer eigenvalues" arxiv: 2401.05291, we associated  with any finite partially ordered set a remarkable matrix depending on parameters. Each matrix element is a variable (which can appear in several places in the matrix) and all eigenvalues are integer linear combinations of variables. I'll explain this result, and also speak about a generalization to convex sets in general reflection groups, and even to the case where there is no group at all.

Personal Website：https://www.ihes.fr/~maxim/

Recording: https://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Matrices_filled_by_Variables_from_Posets_to_Coxeter_Groups_and_Beyond.html