Abstract for the talk on 30.05.2023 (15:00 h)Seminar on Nonlinear Algebra
Hendrik Süß (Friedrich-Schiller-Universität Jena)
Dually Lorentzian Polynomials
30.05.2023, 15:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, G3 10 (Lecture hall)
Lorentzian polynomials, recently introduced by Brändén and Huh, have coefficients that satisfy a form of log-concavity, and have been used to prove, reprove, and conjecture various combinatorial statements coming
from convex geometry, representation theory, and the theory of matroids. Accepting that being Lorentzian is a useful concept, it is natural to ask for differential operators (with constant coefficients) that preserve this property. This leads to the notion of dually Lorentzian polynomials. As an application of this observation, I will show how
dually Lorentzian polynomials give rise to generalisations of the Alexandrov-Fenchel inequality in convex geometry.
This is joint work with Julius Ross and Thomas Wannerer.