Nikita Nekrasov

Nikita Nekrasov
Name	Nikita Nekrasov
Birth date	1973
Birth place	Moscow, Russian SFSR, Soviet Union
Nationality	Russian
Fields	Mathematical physics, Quantum field theory, String theory, Algebraic geometry
Institutions	Institut des Hautes Études Scientifiques, University of Cambridge, Harvard University, Rutgers University, Simons Center for Geometry and Physics
Alma mater	Moscow State University, Institute for Nuclear Research (Russia)
Doctoral advisor	Arkady Vainshtein
Known for	Instanton counting, Seiberg–Witten theory, Nekrasov partition function, Omega background

Nikita Nekrasov is a mathematical physicist noted for foundational contributions to quantum field theory, string theory, and algebraic geometry. He formulated powerful techniques connecting supersymmetric gauge theories to enumerative geometry and integrable systems, producing tools widely used across Seiberg–Witten theory, Donaldson–Thomas theory, and Gromov–Witten invariants. His work bridges research traditions associated with Edward Witten, Alexander Polyakov, Anton Kapustin, and collaborators at institutions such as IHÉS and Harvard University.

Early life and education

Born in Moscow during the late Soviet era, he undertook early studies at Moscow State University and completed graduate work at the Institute for Nuclear Research (Russia), where his doctoral training placed him in the lineage of researchers influenced by Lev Landau, Isaak Pomeranchuk, and Arkady Vainshtein. His formation combined exposure to Russian schools of theoretical physics and international centers such as CERN and Stony Brook University, leading to interactions with figures like Andrei Losev and Sergei Gukov. During this period he cultivated expertise in supersymmetric gauge theories, instanton calculus, and methods later central to the development of the Nekrasov partition function.

Research contributions and career

Nekrasov introduced a set of techniques—most notably the Nekrasov partition function and the Omega background—that provided exact formulae for prepotentials in supersymmetric gauge theories, affecting research threads associated with Seiberg–Witten prepotential, instanton moduli space, and equivariant localization. These constructions linked to mathematical programs such as Donaldson theory, Seiberg–Witten invariants, and Gromov–Witten theory, and interfaced with developments in topological string theory and matrix models. His work established correspondences between four-dimensional N=2 supersymmetric gauge theories and two-dimensional conformal field theories, interacting with the body of results around the AGT correspondence and contributions by Luis Alday, Davide Gaiotto, and Yuji Tachikawa.

He has contributed to the understanding of quantum integrable systems via connections to the Bethe ansatz and Yangian structures, resonating with research of Alexander Belavin, Vladimir Drinfeld, and Evgeny Sklyanin. Nekrasov's methods have informed exact computations in topological field theory and clarified aspects of non-perturbative dynamics described in works by Nathan Seiberg and Edward Witten. His career includes significant periods at Rutgers University, Harvard University, the Institute for Advanced Study, and the Institut des Hautes Études Scientifiques, where he collaborated with mathematicians and physicists across Caltech, Princeton University, and Columbia University.

Major publications and selected works

Key publications include his foundational papers on instanton counting and the Nekrasov partition function, which articulate the Omega background technique and compute exact low-energy effective actions in N=2 theories. These works intersect with literature on Seiberg–Witten theory and the mathematical treatment of moduli spaces pioneered by Simon Donaldson and Kronheimer and Nakajima. Subsequent papers explore relations to the AGT correspondence, developments in Donaldson–Thomas invariants, and the role of noncommutative geometry in gauge theory, connecting to research by Maxim Kontsevich, Nigel Hitchin, and Kontsevich–Soibelman collaborators. He has also published on connections between supersymmetric indices, wall-crossing phenomena, and stability conditions studied by Tom Bridgeland and Philippe Di Francesco.

Representative titles: - "Seiberg–Witten prepotential from instanton counting" — seminal article establishing exact instanton sums. - Works on the Omega background and localization — formalizing equivariant techniques in gauge theory. - Papers connecting gauge theory partition functions to conformal blocks in two-dimensional Liouville field theory and beyond, contributing to the AGT corpus.

Awards and honors

Nekrasov has received recognition from multiple scientific bodies for his influence on mathematical physics. Honors include invitations to major addresses at International Congress of Mathematicians events, membership and fellowships at research centers such as IHÉS and the Institute for Advanced Study, and awards reflecting impact on both mathematics and physics communities alongside peers like Maxim Kontsevich and Edward Witten. He has been cited in award citations and invited lectures at institutions including Cambridge University and Princeton University.

Academic positions and collaborations

Throughout his career he has held positions at leading institutions: faculty and visiting roles at Rutgers University, Harvard University, Princeton University, and research appointments at IHÉS and the Institute for Advanced Study. He has collaborated with a wide network including Andrei Okounkov, Rahul Pandharipande, Anton Kapustin, Dmitry Koroteev, Andrey Smirnov, and contributors to the AGT program such as Davide Gaiotto and Luis Alday. His collaborative work spans seminars and programs at Simons Center for Geometry and Physics, Mathematical Sciences Research Institute, and international conferences at venues like CERN and the Perimeter Institute.

Influence and legacy in mathematical physics

Nekrasov's techniques have become standard tools in modern mathematical physics, underpinning exact computations in supersymmetric theories and stimulating advances in enumerative geometry, representation theory, and integrable systems. His influence permeates research on the AGT correspondence, Donaldson–Thomas theory, and modern treatments of moduli spaces, impacting continued work by scholars in algebraic geometry and string theory communities associated with Princeton University, Harvard University, and IHÉS. The Nekrasov partition function remains central to ongoing research programs linking quantum field theory to geometry and topology, forming a durable legacy that continues to inspire cross-disciplinary collaboration.

Category:Mathematical physicists Category:Russian physicists