Lorentzian Polynomials and the Incidence Geometry of Tropical Linear Spaces

Explore a one-hour seminar presentation delving into the relationship between Lorentzian polynomials and tropical linear spaces geometry. Learn how proper position, a fundamental concept in stable polynomial theory, extends beyond real root interlacing into higher dimensions through a Lorentzian perspective. Examine the moduli space of codimension-1 tropical linear subspaces and discover how its geometric properties connect to Lorentzian polynomials. Understand the bidirectional relationship where Lorentzian polynomials reveal geometric insights about moduli spaces, while incidence problem solutions uncover new convex cones of Lorentzian polynomials. Presented by Jayden Wang from the University of Texas at Austin at the Institute for Advanced Study's Special Year Seminar II.