Hao Shen

Hao Shen is a Professor in the Department of Mathematics at the University of Wisconsin-Madison. His academic work focuses on stochastic partial differential equations and their connections with quantum field theory, statistical mechanics, and geometric flows.

Dr. Shen's educational background includes a PhD from Princeton University in 2013 under the supervision of Weinan E. He completed postdoctoral training at the University of Warwick with Martin Hairer (2014-2015) and served as a Ritt Assistant Professor at Columbia University with Ivan Corwin (2015-2018) before joining UW-Madison.

Hao Shen's research interests span multiple areas of mathematical physics and probability theory:

• Stochastic partial differential equations (SPDEs)
• Quantum field theory, particularly Yang-Mills theory and gauge theories
• Statistical mechanics and interacting particle systems
• Geometric flows, including Ricci flow
• Stochastic quantization methods
• Renormalization theory for singular SPDEs

His recent publications demonstrate a strong focus on the mathematical foundations of quantum field theories through stochastic methods, with particular attention to Yang-Mills theory in various dimensions and the O(N) sigma model. Shen's work often bridges rigorous mathematical analysis with physical applications, employing advanced techniques from regularity structures, paracontrolled distributions, and stochastic analysis.

• Simons Fellow in Mathematics (2024-2025)
• NSF CAREER DMS-2044415 (2021-2026)
• NSF DMS-1954091 (2020-2023)
• NSF DMS-1712684 / DMS-1909525 (2017-2020)

As an academic leader, Dr. Shen serves on the editorial boards of prestigious journals including Annals of Probability, Stochastics and Partial Differential Equations: Analysis and Computations, and Annales de l'Institut Henri Poincaré. He actively contributes to the mathematical community through organizing conferences and summer schools, such as the 2024 MSRI/SLMath Summer Graduate School on "Stochastic quantization" and the upcoming 2025 SLMath semester program "Recent Trends in Stochastic Partial Differential Equations."

Dr. Shen's teaching portfolio includes advanced courses in probability theory, stochastic analysis, and specialized topics in stochastic partial differential equations. His commitment to education is evident in his development of graduate-level courses that bridge theoretical mathematics with applications in physics.