Connections to Schubert Calculus Learning Seminar
3:30pm|Simonyi 101
Topic: Three Proofs Of The Reverse Khovanskii-Teissier Inequality
Speaker: Sergio Cristancho
Affiliation: Princeton University
Date: January 22, 2025
The reverse Khovanskii-Teissier inequality is a three term inequality for nef divisors which first appeared in the context of Kähler geometry. It provides an upper bound on a product of two divisors in terms of products with the third, hence its ‘reverse` nature in contrast with the usual Khovanskii-Teissier inequality. The first to observe such inequality were Xiao (’16) and Popovici (’15) while studying Morse type inequalities. Afterwards, Lehman and Xiao (’16) proved an analogous inequality for mixed volumes of convex bodies; and Jiang and Li (’23) proved the same inequality for projective varieties using Okounkov bodies. The aim of this talk will be to present the three instances of the reverse Khovanskii-Teissier inequality and their proofs: analytic, algebraic, and convex geometric.