The Space of Lorentzian Polynomials

Explore the mathematical realm of Lorentzian polynomials in this 59-minute lecture by June Huh from Princeton University. Delve into topics such as projective varieties, continuous and discrete convexity, quadratic forms, and discrete convex analysis. Examine the concepts of M-convexity, compact and discrete sets, and nonnegative coefficients. Gain insights into algebraic intuition, concave functions, polynomials, and fractional derivatives. Presented as part of the "Beyond Randomized Rounding and the Probabilistic Method" series at the Simons Institute, this talk offers a deep dive into advanced mathematical concepts and their applications.

Introduction
Projective varieties
Continuous and discrete convexity
Quadratic forms
Discrete convex analysis
M convexity
Compact set
Discrete set
Nonnegative coefficients
Algebraic intuition
Concave functions
Polynomials
Fractional Derivatives