Stony Brook University Professor Nikita Nekrasov has been named a Principal Investigator in the newly established Simons Collaboration on Probabilistic Paths to Quantum Field Theory. The initiative, directed by Professor Scott Sheffield of the Massachusetts Institute of Technology, brings together 14 researchers from different countries to develop a unified probabilistic approach to quantum field theory (QFT).
The collaboration focuses on integrating probability, analysis, and mathematical physics to address problems within QFT. Members aim to create a rigorous probabilistic foundation for QFT in Euclidean space, building on recent progress in stochastic analysis and random geometry.
“In recent times, probability theory has made enormous strides, to the point that it provides novel, powerful and insightful approaches to very deep problems in quantum field theory and statistical mechanics,” said Luis Alvarez-Gaume, Professor and Director of the Simons Center for Geometry and Physics. “Together with independent advances on the theoretical physics side we are witnessing an extremely fertile framework to address fundamental problems in our understanding of the most basic language to express the laws of nature: quantum field theory. We are proud that Professor Nikita Nekrasov is playing a leading role, spearheading Stony Brook’s role in this exciting project.”
According to information from the Simons Foundation, developments such as conformally invariant processes—including Schramm–Loewner evolution—have helped analyze fractal structures within field theories. Other tools like regularity structures have clarified field singularities, while multiplicative chaos has advanced mathematical foundations for Liouville quantum gravity. Combining these methods through frameworks like mating-of-trees has produced notable results in statistical physics.
The Simons Collaboration seeks to further enable non-perturbative study of major models at the intersection of mathematics and quantum field theory by advancing this unified probabilistic perspective.
“Einstein famously objected to quantum mechanics, remarking that ‘God doesn’t play dice,’ as he resisted the theory’s inherently probabilistic nature. Yet, despite his doubts, quantum field theory — though still lacking complete mathematical foundations — has become the most precise description of nature we possess,” said Professor Nekrasov. “The goal of this collaboration is to build those very foundations, paradoxically, through the tools of probability theory. This joint effort continues the Stony Brook tradition of deep interaction between physicists and mathematicians, a legacy reaching back to C.N. Yang and J.H. Simons.”
Nekrasov is recognized for his work in quantum field theory and string theory. He is among the founding faculty at Stony Brook’s Simons Center for Geometry and Physics and holds a professorship at its Yang Institute for Theoretical Physics. After earning his PhD at Princeton University under Nobel laureate David Gross’s supervision, Nekrasov held a permanent position at France’s Institut des Hautes Études Scientifiques before joining Stony Brook in 2013. His honors include awards from French Academy of Sciences (Prix Jacques Herbrand), Hermann Prize (2004), Compositio Prize (2009), and Dannie Heineman Prize in Mathematical Physics from the American Physical Society (2023).
This marks Stony Brook’s second participation in a Simons Collaboration related to mathematics and physics; previously, members including Professors Leonardo Rastelli (director) and Zohar Komorgodski were involved with The Simons Collaboration for the Nonperturbative Bootstrap alongside researchers from other institutions.
