Title: Volume inequalities and volume polynomials

Abstract: Many classical geometric inequalities, such as the isoperimetric inequality and the Loomis-Whitney inequality, can be understood and generalized using mixed volumes. In this talk, I will explain how these inequalities fit into a broader framework based on volume polynomials, which naturally relate mixed volume inequalities to intersection number inequalities in algebraic geometry. This perspective provides a unified approach to a wide range of classical results and leads to new generalizations of mixed volume inequalities. This is joint work with June Huh, Mateusz Michałek and Jian Xiao.