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Colloquium by Jonathan Leake (Technische Universität Berlin): Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture

Nov 22, 2021 | 04:00 PM s.t.

About 5 years ago, the Heron-Rota-Welsh conjecture (log-concavity of the coefficients of the characteristic polynomial of a matroid) was proven by Adiprasito, Huh, and Katz via the exciting 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 Heron-Rota-Welsh conjecture. Our proof uses an extension of the theory of Lorentzian polynomials to convex cones. In this talk, I will briefly discuss the basics of Lorentzian (aka completely log-concave) polynomials, and then I will give an overview of our new proof of the Heron-Rota-Welsh conjecture.

Time & Location

Nov 22, 2021 | 04:00 PM s.t.

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
Room MA 041 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)