Convexity Seminar

---

A realization problem for mixed volumes in R^4

Speaker: Shouda Wang, Princeton University

Location: Warren Weaver Hall 1302

Date: Tuesday, March 3, 2026, 11 a.m.

Synopsis:

Mixed volumes of convex bodies encode fundamental geometric quantities such as volume, surface area, and projection volumes. Many classical inequalities are known, including the Alexandrov–Fenchel and Loomis–Whitney inequalities. A natural realization problem asks whether these inequalities capture all constraints among mixed volumes. In this talk I will present new progress in this direction: in particular, we give a complete characterization of the sextuples that arise as the areas of the six 2-dimensional coordinate projections of a convex body in $R^4$. This is joint work with Daoji Huang, June Huh, Mateusz Michałek, and Botong Wang.