Math Labs

John Pardon

fl. 1989, Chapel Hill, North Carolina, United States

GeometryTopologyClay Research Award 2022Fields Medal 2026

American geometer and topologist, permanent member of the Simons Center for Geometry and Physics at Stony Brook; Fields Medalist 2026.

John Vincent Pardon was born in 1989 in Chapel Hill, North Carolina, the son of a mathematics professor at Duke University and a math teacher. He won three gold medals at the International Olympiad in Informatics (2005–2007) and, while an undergraduate at Princeton, solved a 1983 problem of Gromov by showing that certain torus knots cannot be embedded in space with bounded stretch factor — work published in the Annals of Mathematics that earned him the 2012 Morgan Prize. He graduated as valedictorian in 2011.

He completed his PhD at Stanford in 2015 under Yakov Eliashberg and was named a Clay Research Fellow the same year. After a year as assistant professor at Stanford he became full professor at Princeton in 2016, then moved in 2022 to the Simons Center for Geometry and Physics at Stony Brook University, where he is a permanent member.

Pardon's work repeatedly supplies the foundations other researchers need: his alternative construction of virtual fundamental cycles made large parts of symplectic geometry more rigorous and accessible, his series with Ganatra and Shende established structural results for wrapped Fukaya categories, and his proof of the MNOP conjecture unified two major curve-counting theories. In topology he solved Gromov's knot distortion problem and proved the Hilbert–Smith conjecture for 3-manifolds. He received the Clay Research Award in 2022 and the Fields Medal in 2026.

Workplaces: Simons Center for Geometry and Physics, Stony Brook University, Princeton University

United States

Award-winning work

Fields Medal 2026Pardon was awarded the medal for his achievements in symplectic geometry, including new approaches to virtual fundamental cycles, Fukaya categories of certain manifolds, and counting holomorphic curves, and for contributions to other areas of geometry and topology, including group actions on 3-manifolds and knot theory. He imported techniques from algebraic topology to give an alternative construction of virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves, applying it to a proof of the Arnold conjecture and a definition of contact homology. With Ganatra and Shende he computed wrapped Fukaya categories of non-compact symplectic manifolds conjectured by Kontsevich and Nadler, and he proved the 70-year-old Hilbert–Smith conjecture for group actions on 3-manifolds. Most recently he proved the Maulik–Nekrasov–Okounkov–Pandharipande conjecture relating Gromov–Witten and Donaldson–Thomas invariants of Calabi–Yau threefolds.

Contributions, linked to the library

Library topicSymplectic geometryProvided new foundations for pseudo-holomorphic curve theory — virtual fundamental cycles and wrapped Fukaya categories — and proved the Arnold and MNOP conjectures.Library topicKnot theorySolved Gromov's problem on the distortion of torus knots as an undergraduate, showing the stretch factor can be arbitrarily large.