Lorentzian polynomials serve as a bridge between continuous and discrete convex analysis, with tropical geometry providing the critical link. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions, leading for example to a short proof of Mason's conjecture on the number of independent sets of a matroid. This lecture series will explore the intricate relationships among Grassmannians over hyperfields, dequantization processes, and the theory of Lorentzian polynomials. In ongoing collaborative work with Matt Baker, Mario Kummer, and Oliver Lorscheid, we extend the connection between Lorentzian polynomials and discrete convex functions to matroids over triangular hyperfields, as introduced by Viro. This extension deepens our understanding of the space of Lorentzian polynomials, revealing a complex interplay among analysis, combinatorics, and geometry.

The three lectures in this series are designed to be accessible to a broad audience and appropriate for a Department Colloquium.

Among his many honors, Prof. Huh is a recipient of the Fields Medal (2022), the MacArthur Fellowship (2022), and the New Horizons in Mathematics Prize (2019). He received his PhD in Mathematics from U-M in 2014.