Yu Deng

Native spelling: 邓煜

fl. 1989, Kaifeng, Henan, China

Differential equations and dynamical systemsProbability and statisticsMathematical physicsClay Research Award 2026Fields Medal 2026

Chinese mathematician at the University of Chicago working on nonlinear dispersive PDEs and kinetic theory; Fields Medalist 2026.

Yu Deng was born in Kaifeng, Henan, China, and raised in Shenzhen. A talented Go player as a child, he turned fully to mathematics after missing qualification for the national Go tournament, winning a gold medal at the 2006 International Mathematical Olympiad at age 16. He studied at Peking University before transferring to MIT, graduating in 2011, and earned his PhD at Princeton University in 2015 under Alexandru Ionescu.

After an instructorship at the Courant Institute (2015–2018) he became assistant professor at the University of Southern California, rising to full professor in 2024, then moved to the University of Chicago the same year, where he was promoted to full professor in 2025.

Deng's research links microscopic dynamics to statistical and macroscopic laws. His derivation, with Hani and Ma, of the Boltzmann equation from Newtonian hard-sphere dynamics resolves a challenge dating back 125 years and connects, via earlier Boltzmann-to-Navier–Stokes limits, particle motion to fluid behavior — a major case of Hilbert's sixth problem. His wave-turbulence work gives a rigorous foundation to the kinetic equations physicists use to describe interacting waves. He received the Clay Research Award and the Fields Medal in 2026; he and Hong Wang are the first Chinese citizens to win the medal.

Workplaces: University of Chicago

China, United States

Award-winning work

Clay Research Award 2026For the remarkable derivation of the Boltzmann equation for long times, starting from a system of hard spheres.

Fields Medal 2026Deng was awarded the medal for his work in partial differential equations, including the rigorous derivation of the Boltzmann equation from hard-sphere dynamics for rarefied gases, the derivation of wave kinetic equations from nonlinear dispersive systems, and probabilistic approaches to nonlinear Schrödinger dynamics. With Zaher Hani and Xiao Ma he derived Boltzmann's equation from deterministic particle dynamics in the low-density regime for as long as the Boltzmann solution exists, overcoming the repeated-collision problem that had limited Lanford's theorem to very short times and advancing a key case of Hilbert's sixth problem. With Hani he rigorously derived the wave kinetic equation of wave turbulence theory from nonlinear dispersive equations over the time scales predicted by physics. With Nahmod and Yue he developed random-tensor and random-averaging-operator methods yielding new results on long-time behavior and Gibbs measure invariance for nonlinear Schrödinger equations.

Contributions, linked to the library

Great problemHilbert's sixth problemHis derivation of the Boltzmann equation — and hence, via known limits, of fluid equations — from particle dynamics is a major advance on Hilbert's sixth problem.Library topicThe wave equationRigorously derived wave kinetic equations of turbulence theory from nonlinear dispersive equations such as the nonlinear Schrödinger equation.Library topicThe Navier–Stokes equationsCombined with Boltzmann-to-fluid limits, his hard-sphere derivation links microscopic particle motion to the Navier–Stokes equations.