A matrix is totally positive if all of its minors are totally positive. It may not be obvious that non-trivial examples of such matrices even exist. However, we will give a bijection between totally positive $n \times n$ matrices and $\mathbb{R}_{>0}^n$. On our way to describing parametrizations of such matrices, we will prove Lindstrom's Lemma, which is a combinatorial tool that relates planar networks to minors of a corresponding weight matrix.

This talk will be accessible to all grad students in the department. Speaker(s): Umang Varma (UM)