Postnikov–Stanley polynomials are Lorentzian, Katherine Tung (Harvard) -- Friday, June 6th, 2025

The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, Mészáros, and St. Dizier in 2022. We give an alternative, elementary proof of this result, explicitly characterize the Newton polytopes of dual Schubert polynomials, and provide a polynomial-time algorithm for determining if a dual Schubert polynomial coefficient vanishes. We furthermore generalize the M-convexity result by showing that Postnikov–Stanley polynomials, also called skew dual Schubert polynomials, are Lorentzian. This work is contained in papers arXiv:2411.16654 and arXiv:2412.02051, joint with Serena An and Yuchong Zhang.

Organizers: Ian Cavey, Andrew Hardt, Alexander Yong