Stony Brook University Professor Nikita Nekrasov has been named a Principal Investigator in the newly launched 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 various countries to advance the mathematical understanding of quantum field theory (QFT).
The collaboration focuses on developing a unified probabilistic framework for QFT in Euclidean space. It aims to connect probability, analysis, and mathematical physics to address foundational questions in the field. Recent advances in stochastic analysis and random geometry have provided new tools for examining non-perturbative aspects of QFT. For example, conformally invariant processes such as Schramm–Loewner evolution help analyze fractal structures within field theories, while the theory of regularity structures sheds light on singularities in these fields. Multiplicative chaos contributes to the mathematical basis for Liouville quantum gravity, and approaches like mating-of-trees combine these tools for significant results in statistical physics.
Luis Alvarez-Gaume, Professor and Director of the Simons Center for Geometry and Physics at Stony Brook University, commented on the importance of this development: “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.”
According to information from the Simons Foundation, creating a probabilistic foundation for Euclidean QFT will allow researchers to perform rigorous non-perturbative analysis of key models and strengthen connections between mathematics and quantum field theory.
Professor Nekrasov reflected on both historical context and future goals: “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 is among the founding faculty members 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 University full-time in 2013. His honors include awards from both French scientific institutions and international societies.
This marks Stony Brook's second participation in a Simons Collaboration focused on mathematics and physics; previously, faculty members contributed leadership roles within The Simons Collaboration for the Nonperturbative Bootstrap.