Stony Brook University Professor Nikita Nekrasov has been named a Principal Investigator in the Simons Collaboration on Probabilistic Paths to Quantum Field Theory. The initiative, launched by the Simons Foundation, will be directed by Professor Scott Sheffield of the Massachusetts Institute of Technology and will involve 14 researchers from various institutions.
The collaboration aims to unite experts in probability, analysis, and mathematical physics to address problems in quantum field theory (QFT). The researchers will work toward developing a unified probabilistic foundation for QFT 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 information from the Simons Foundation, progress over recent decades in stochastic analysis and random geometry has enabled rigorous study of non-perturbative aspects of QFT. Techniques such as Schramm–Loewner evolution help analyze fractal structures within field theories. Other mathematical frameworks like regularity structures give insight into singularities found within fields, while multiplicative chaos contributes foundational understanding for Liouville quantum gravity. Combined methods such as mating-of-trees have also led to significant results within statistical physics.
By establishing a common probabilistic base for Euclidean QFT, members hope their work will allow deeper non-perturbative analysis of central models and strengthen links between mathematics and quantum field theory.
“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 specializes in quantum field theory and string theory at Stony Brook University’s Department of Physics and Astronomy as well as at its Yang Institute for Theoretical Physics. He helped establish Stony Brook’s Simons Center for Geometry and Physics after earning his doctorate from Princeton University under Nobel laureate David Gross. Prior roles include serving as professor at France’s Institut des Hautes Études Scientifiques (IHES). Among his honors are awards from French Academy of Sciences (Prix Jacques Herbrand), Compositio Prize (2009), Hermann Prize (2004), and Dannie Heineman Prize in Mathematical Physics from American Physical Society (2023).
This marks Stony Brook’s second involvement with a Simons Collaboration in Mathematics and Physics through its faculty at both Yang Institute for Theoretical Physics and Simons Center for Geometry and Physics; previous participants included Professors Leonardo Rastelli (director) and Zohar Komorgodski.
Simons Collaborations bring together research groups focused on important scientific topics; these collaborations may receive up to $2 million annually over four years with possible extension through grants managed by Simons Foundation International.
Stony Brook University is recognized as New York’s flagship public university within SUNY system with more than 26,000 students enrolled. It ranks among top U.S universities according to U.S News & World Report Best Colleges listing (https://www.usnews.com/best-colleges/stony-brook-university-suny-1960). As one out of only eight universities helping manage a national laboratory—Brookhaven National Laboratory—it plays a significant role regionally through research activity contributing almost $8.93 billion annually in economic output (https://www.stonybrook.edu/about/facts-and-rankings/). In 2023 it was named anchor institution for The New York Climate Exchange on Governors Island (https://nyclimateexchange.org/).
