Nikita Nekrasov Chosen as Part of Simons Collaboration on Probabilistic Paths to Quantum Field Theory

Stony Brook University Professor Nikita Nekrasov, in the Department of Physics and Astronomy in the College of Arts and Sciences, has been selected as a Principal Investigator (PI) as part of the Simons Foundation launch of the Simons Collaboration on Probabilistic Paths to Quantum Field Theory. Professor Scott Sheffield, from the Massachusetts Institute of Technology, will direct this new collaboration. Professor Nekrasov will serve on this initiative with 13 other researchers from around the world.

This collaboration will bring together experts in probability, analysis and mathematical physics to work on problems related to quantum field theory (QFT), a theoretical framework uniting the principles of classical field theory, quantum mechanics and special relativity. Collaboration members will work toward a unified probabilistic foundation for quantum field theory in Euclidean space.

“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 Professor and Director of the Simons Center for Geometry and Physics (SCGP) Luis Alvarez-Gaume. “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 the Simons Foundation, in recent decades, substantial advances in stochastic analysis and random geometry have introduced powerful probabilistic tools for rigorously addressing non-perturbative aspects of QFT. Conformally invariant processes like the Schramm–Loewner evolution allow analysis of the fractal structure of field theories, the theory of regularity structures offers insights into field singularities, and multiplicative chaos provides a mathematical foundation for Liouville quantum gravity. Frameworks such as the mating-of-trees approach exemplify how these tools can be fruitfully combined, yielding deep, rigorous results in statistical physics.

By developing a unified probabilistic foundation for Euclidean QFT, the Simons Collaboration on Probabilistic Paths to Quantum Field Theory aims to enable non-perturbative analysis of central models and advance the interface between QFT and mathematics.

“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.”

Professor Nekrasov is a theoretical physicist exploring quantum field theory and string theory. He is a founding faculty member of the Simons Center for Geometry and Physics, and professor at the Yang Institute for Theoretical Physics at Stony Brook. Nekrasov earned his PhD from Princeton University under the supervision of Professor David Gross (Nobel Prize winner, 2004). He was a permanent professor at the Institut des Hautes Études Scientifiques in France before permanently joining Stony Brook in 2013. He was awarded the Prix Jacques Herbrand by the French Academy of Sciences and the Hermann Prize in 2004, the Compositio Prize in 2009, and the Dannie Heineman Prize in Mathematical Physics by the American Physical Society in 2023.

This is the second Simons Collaboration in Mathematics and Physics represented at Stony Brook by members of the Yang Institute for Theoretical Physics and the Simons Center.  The first, The Simons Collaboration for the Nonperturbative Bootstrap, included Professors Leonardo Rastelli as director and Zohar Komorgodski as a PI, along with participants from other institutions.