Jonathan Leake, Technische Universität Berlin, Germany

PDL C38 and via Zoom Link: https://washington.zoom.us/j/91547335974
Abstract:
About 5 years ago, the HeronRotaWelsh conjecture (logconcavity of the coefficients of the reduced characteristic polynomial of a matroid) was proven by Adiprasito, Huh, and Katz via the development of a new combinatorial Hodge theory for matroids. In very recent work with Petter Brändén, we have given a new short "polynomial proof" of the HeronRotaWelsh conjecture. Our proof uses an extension of the theory of Lorentzian polynomials to convex cones, and in particular reproves the HodgeRiemann relations of degree one for the Chow ring of a matroid. In the preseminar, I will discuss the basics of Lorentzian (aka completely logconcave) polynomials as developed by AnariLiuOveis GharanVinzant and by BrändénHuh in recent years. In the remainder of the talk, I will give an overview of our new proof of the HeronRotaWelsh conjecture, emphasizing newly developed tools in the theory of Lorentzian polynomials.
Note: This talk begins with a preseminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974