Nikita Nekrasov, a professor at Stony Brook University’s Simons Center for Geometry and Physics and the C.N. Yang Institute for Theoretical Physics, has been awarded the 2023 Dannie Heineman Prize for Mathematical Physics by the American Institute of Physics (AIP) and the American Physical Society (APS).
Nekrasov received the prestigious prize “for the elegant application of powerful mathematical techniques to extract exact results for quantum field theories, as well as shedding light on integrable systems and non-commutative geometry.”
The annual award acknowledges significant contributions to the field of mathematical physics and will be presented at an upcoming APS meeting.
“We are very happy that Professor Nekrasov was awarded this amply merited recognition — probably the highest recognition in mathematical physics,” said Luis Álvarez-Gaumé, director of the Simons Center for Geometry and Physics. “He has made groundbreaking contributions in several areas of advanced quantum field theory, integrable systems, and in the use of powerful mathematical techniques to shed light into rather deep areas of field theory and string theory. The Simons Center is a late comer in the time-honored tradition representing the fertile interaction between physics and mathematics over millennia. His work represents deep and important chapters in this ongoing mutual inspiration between these inseparable disciplines.”
Nekrasov used techniques from topology to solve important problems in theoretical physics, namely, exactly calculating the effects of the strong force holding together nuclei.
Complex problems in quantum physics are often broken into two pieces: an explicit solution of a simpler system and the analysis of a “perturbation” that reflects the small difference of a realistic model from that simple system. As an example, in a simplified picture, freely propagating particles occasionally meet and interact with other particles along their way. Having many successive interactions is less likely, which makes the perturbation terms mathematically manageable. However, some natural phenomena, such as the strong force, do not follow this rule and require a different approach.
“One needs better understanding of how to account for the effects of strong force,” said Nekrasov. “I found a class of theories for which this can be done exactly, but you have to bring in a novel type of mathematics: topology and non-commutative geometry.”
The mathematics can also be used for exactly solvable models describing many-body interactions, be it planets in the solar system, cold atoms or electrons in a quantum Hall effect. Nekrasov discovered that, under the assumption of supersymmetry, the mathematics of strong interactions is the same as the mathematics describing many particles living on a line and interacting with some repulsive force.
“Instead of trying to visualize the quarks and gluons inside an atomic nucleus, which we cannot see directly, you could set up a laboratory with quantum wires, do some measurements, and then try to translate that result to the world of elementary particles,” Nekrasov said. “That’s the amazing fact about physics and mathematics. There are unexpected connections between different fields.”
A French-Russian national, Nekrasov grew up in Russia, where he became hooked on string theory and mathematical physics after reading a Scientific American article by Professor Michael Green (recipient of 2002 Dannie Heineman Prize for Mathematical Physics). He earned his PhD at Princeton University and completed a postdoctoral fellowship at Harvard University as a junior fellow at the Harvard Society of Fellows. After briefly returning to Princeton University as a Dicke Fellow, he became professor at the Institut des Hautes Études Scientifiques in France. Since 2013, he has been a professor at the Simons Center for Geometry and Physics and the C.N. Yang Institute for Theoretical Physics, which is part of the Department of Physics and Astronomy in the College of Arts and Sciences.
“It’s an honor to receive this award, and in some sense, it’s a way to shake hands with a lot of my heroes, the people who inspired me in my work,” said Nekrasov.
Nekrasov hopes to continue connecting abstract mathematics to theoretical physics and is currently interested in finding applications of quantum field theory to number theory.
“We are so pleased to recognize Nikita Nekrasov with this award,” said Michael Moloney, CEO of AIP. “His work has taken abstract principles in mathematics and proved them essential for theoretical physics, building upon our fundamental knowledge of how the universe works — the pondering on which has been an inspiration to generations of scientists.”