Title: “Polynomials with Lorentzian signature over cones”

Abstract: Over the past decade, there has been a notable effort to fuse the techniques of algebraic geometry and combinatorics, crafting a comprehensive framework for addressing long-standing conjectures in theoretical computer science and matroid theory pertaining to unimodality and log-concavity. This endeavor includes an exploration of Lorentzian polynomials, also known as completely log-concave or strongly log-concave polynomials, which establishes a bridge between discrete and continuous convexity.

In this talk, I shall give a panoramic view of my research work focusing on the exploration of Lorentzian polynomials. I will introduce the concept of polynomials with Lorentzian signature (PLS) defined over convex cones, representing a natural extension of the remarkable class of Lorentzian polynomials.

The Discrete Math Seminar (DMS) is intended for Kennesaw State faculty working in the various areas of algebra, number theory, and discrete mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone who is interested in attending. This talk will take place in a hybrid format – in-person in D-112 or virtually.

]]>