Petter Brändén: Lorentzian polynomials and the symmetric exclusion process

ABSTRACT: Lorentzian polynomials link discrete and continuous notions of convexity. They have recently been used to prove longstanding conjectures in combinatorics and computer science. The symmetric exclusion process is one of the main models in interacting particle systems. It models particles moving on a finite or countable set in a continuous way. We prove that projective spaces of Lorentzian polynomials are homeomorphic to closed Euclidean balls by utilizing a connection between the symmetric exclusion process and the geometry of polynomials. This solves a conjecture of June Huh and the speaker.