Math Labs

June Huh

Native spelling: 허준이

fl. 1983, Stanford, California, United States

Combinatorics and discrete mathematicsAlgebraGeometryFields Medal 2022

American-South Korean mathematician at Princeton University who created a Hodge theory for matroids; Fields Medalist 2022.

June Huh (Heo Jun-i) was born in Stanford, California, and raised in South Korea, where his father taught statistics. He dropped out of high school to pursue poetry, later completing an equivalency degree, and enrolled at Seoul National University in physics and astronomy before switching to mathematics. An encounter with Fields Medalist Heisuke Hironaka, lecturing in Seoul, drew him to algebraic geometry.

He earned his PhD at the University of Michigan in 2014 under Mircea Mustaţă. After positions at the Institute for Advanced Study, the Clay Mathematics Institute, and Princeton, he became professor at Princeton University, where he remains.

Huh's work revealed that deep structures of algebraic geometry — Hodge theory, the Hard Lefschetz theorem, Hodge–Riemann bilinear relations — persist in purely combinatorial settings such as matroids, objects with no underlying space at all. The resulting theory settled decades-old conjectures of Read, Rota, Heron, Welsh, and Dowling–Wilson on the log-concavity of chromatic and characteristic polynomials, and has found applications in graph theory and coding theory. He received the Fields Medal in 2022.

Workplaces: Princeton University, Institute for Advanced Study, Princeton

United States, South Korea

Award-winning work

Fields Medal 2022Huh was awarded the medal for bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, and the development of the Lorenzian polynomials. With Eric Katz he proved the Heron–Rota–Welsh conjecture — that the coefficients of the characteristic polynomial of a matroid are log-concave — for representable matroids, and with Adiprasito and Katz he established a full Hodge theory (Hard Lefschetz and Hodge–Riemann relations) for the Chow ring of an arbitrary matroid, settling the conjecture in general. His construction shows that matroids, though purely combinatorial objects, behave as if they had a Kähler geometry, reshaping combinatorial algebraic geometry.

Contributions, linked to the library