June Huh will give the SoM Stelson Lecture and a special SoM Colloquium during his visit to GT on September 18-19, 2025.

Stelson Public Lecture

Thursday, September 18, 2025
5:00pm - 6:00pm @ Boggs B5
Reception 4:00-4:45pm in Skiles Courtyard

Projection areas of 4-dimensional convex bodies

Consider a convex body in 4-dimensional space—perhaps an ellipsoid or a polytope. When we project the convex body onto the six coordinate planes, we obtain six planar shadows whose areas we can measure. This leads to a deceptively simple question: which six numbers can arise as these projection areas?

Behind this concrete geometric problem lies a web of deep mathematics connecting Minkowski's classical work on the isoperimetric problem to recent developments in algebraic geometry. I will trace the path to the answer, revealing the rich mathematical landscape that emerges from this seemingly elementary question.

SoM Special Colloquium 

Friday, September 19, 2025
11:00am - 12:00pm
Skiles 006

Volume polynomials

Volume polynomials constitute a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties arising from convex bodies and projective varieties. I will introduce new entropy inequalities satisfied by volume polynomials, discuss applications to the combinatorics of algebraic matroids, introduce the new class of analytic matroids, and pose several open questions (based on joint with Lukas Grund, Mateusz Michalek, Henrik Süss, and Botong Wang).

About the Speaker

Professor June Huh is known for forging deep and unexpected connections between combinatorics and algebraic geometry. His work has transformed how mathematicians think about longstanding problems involving discrete structures, such as graphs and matroids, by importing tools from geometry traditionally used to study curves, surfaces, and other solutions to polynomial equations.

While still a graduate student, Huh resolved Read’s conjecture—a 1968 problem in graph theory—by applying techniques from algebraic geometry to prove a pattern in the coefficients of chromatic polynomials. This breakthrough launched a line of research that culminated in a proof of the Rota-Welsh conjecture with collaborators Karim Adiprasito and Eric Katz, establishing a striking bridge between combinatorics and Hodge theory, a foundational topic in geometry.

With Petter Brändén, Huh also introduced the theory of Lorentzian polynomials, providing a new framework for understanding log-concavity and related phenomena across combinatorics, computer science, and probability. For his groundbreaking contributions bringing ideas from Hodge theory into combinatorics, Huh was awarded a MacArthur Fellowship and the 2022 Fields Medal.

Huh’s current research interests include tropical geometry, Lorentzian polynomials, correlation phenomena for models in statistical physics, connections between realizability problems in algebraic geometry and combinatorics, and the geometry of matroids and polymatroids.