**Abstract:**

Tropicalization is a way to understand the asymptotic behavior of algebraic (or semi-algebraic) sets through polyhedral geometry. In this talk, I will talk about the tropicalization of the principal minors of positive semidefinite matrices. This gives a combinatorial way of understanding their asymptotic behavior and discovering new inequalities on these minors. The resulting tropicalization will be a subset of M-concave functions on the discrete hypercube closely related to the tropical Grassmannian and tropical flag variety. I will not assume any familiarity with tropical geometry or the positive semidefinite cone. This is based on joint work with Abeer Al Ahmadieh, Felipe Rincón, and Josephine Yu.

**Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.**

**Join Zoom Meeting: https://washington.zoom.us/j/ 91547335974Meeting ID: 915 4733 5974**