Stony Brook University Professor Nikita Nekrasov has been named a Principal Investigator in the Simons Collaboration on Probabilistic Paths to Quantum Field Theory, an initiative launched by the Simons Foundation. The collaboration is directed by Professor Scott Sheffield of the Massachusetts Institute of Technology and includes 13 other researchers from institutions worldwide.
The group will focus on developing a unified probabilistic foundation for quantum field theory (QFT) in Euclidean space. QFT combines elements of classical field theory, quantum mechanics, and special relativity, and serves as a fundamental framework for understanding physical laws.
Luis Alvarez-Gaume, Professor and Director of the Simons Center for Geometry and Physics at Stony Brook University, commented on the significance of this work: “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. 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.”
The Simons Foundation notes that recent progress in stochastic analysis and random geometry has introduced new probabilistic tools for studying non-perturbative aspects of QFT. Methods such as Schramm–Loewner evolution help analyze fractal structures within field theories; regularity structures provide insight into singularities; multiplicative chaos underpins Liouville quantum gravity; and frameworks like mating-of-trees combine these approaches for rigorous results in statistical physics.
The collaboration aims to advance mathematical understanding by enabling non-perturbative analysis of central models at the intersection of mathematics and physics.
Professor Nekrasov said: “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. 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 helped found the Simons Center for Geometry and Physics at Stony Brook University and holds a professorship at its Yang Institute for Theoretical Physics. He received his PhD from Princeton University under Nobel laureate David Gross and previously held a permanent position at France’s Institut des Hautes Études Scientifiques before joining Stony Brook in 2013. His honors include awards from the French Academy of Sciences (Prix Jacques Herbrand), Compositio Prize (2009), Hermann Prize (2004), and Dannie Heineman Prize in Mathematical Physics from the American Physical Society (2023).
This marks Stony Brook’s second involvement with a Simons Collaboration in Mathematics and Physics through members affiliated with both its Yang Institute for Theoretical Physics and Simons Center for Geometry and Physics. The first was The Simons Collaboration for the Nonperturbative Bootstrap.
