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| Pestun | |
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| Name | Pestun |
Pestun is a mathematician and theoretical physicist noted for contributions at the intersection of algebraic geometry, representation theory, and quantum field theory. His work has influenced developments in supersymmetry, localization techniques, and the study of gauge theory, connecting rigorous mathematics with ideas from string theory, conformal field theory, and integrable systems. Pestun’s research has been central to collaborations among scholars at institutions such as Institute for Advanced Study, Princeton University, Harvard University, ETH Zurich, and Max Planck Institute for Mathematics.
Pestun was born in Eastern Europe and completed early studies at national institutions before moving to renowned centers for graduate training. He received doctoral and postdoctoral mentorship in environments linked to University of Cambridge, University of Oxford, and research groups associated with European Mathematical Society and Clay Mathematics Institute. During graduate study he engaged with problems related to Donaldson theory, Seiberg–Witten theory, Atiyah–Singer index theorem, and techniques from equivariant cohomology under advisors and collaborators from labs connected to Cambridge Mathematical Tripos, St John's College, Cambridge, and research seminars at Institut des Hautes Études Scientifiques.
Pestun’s career spans faculty and research positions at leading universities and institutes, including appointments that fostered interaction with communities at Princeton University, Harvard University, Perimeter Institute for Theoretical Physics, and Simons Center for Geometry and Physics. His research program synthesizes methods from topological quantum field theory, matrix models, Langlands program, and the mathematics emerging from AdS/CFT correspondence. He has applied localization methods in supersymmetric gauge theories to compute exact quantities in N=2 supersymmetric gauge theory, linking to results in instanton counting, Nekrasov partition function, and the AGT correspondence. Collaborations with researchers affiliated with Max Planck Institute for Mathematics, IHES, and research groups at University of California, Berkeley and University of Chicago expanded the interplay between physical intuition and mathematical rigor in his work.
Pestun developed techniques that employ equivariant localization on spaces of fields and moduli of instantons, connecting to the structure of moduli space of flat connections, Hitchin system, and Chern–Simons theory. These methods enabled explicit evaluations of observables such as Wilson loops and partition functions on curved manifolds like four-sphere and compactifications studied in Seiberg–Witten theory. His research built bridges to the Geometric Langlands program, influencing threads connecting vertex operator algebras, modular forms, and categorical aspects explored at venues like Institute for Advanced Study and conferences organized by Mathematical Sciences Research Institute.
Pestun is widely cited for pioneering computations of exact expectation values in supersymmetric gauge theories using localization on the four-sphere and for clarifying relations between perturbative and nonperturbative sectors via instanton calculus. Key contributions include rigorous formulations of localization in the presence of supersymmetric background fields, precise evaluation of matrix model integrals related to partition functions, and the demonstration of connections between supersymmetric observables and integrable models studied at Simons Center workshops. His publications have appeared in leading journals alongside work from collaborators at Harvard University, Princeton University, Stanford University, Yale University, and Columbia University.
Pestun’s results influenced subsequent work on exact results in three-dimensional supersymmetric theories, relations to Chern–Simons theory and knot invariants studied by researchers at Rutgers University and University of Oxford, and extensions of localization to theories with various amounts of supersymmetry developed in groups at ETH Zurich and Imperial College London.
Pestun has received recognition from international mathematical and physical societies and has been invited to lecture at prestigious gatherings such as the International Congress of Mathematicians, workshops at Mathematical Sciences Research Institute, and seminars at Institute for Advanced Study. He has been supported by fellowships and grants from organizations including the Simons Foundation, European Research Council, and national science agencies connected to universities like Princeton University and Harvard University. Honors include invited plenary and sectional lectures at conferences hosted by the American Mathematical Society and the Royal Society.
Pestun maintains collaborations with a broad network of mathematicians and physicists across institutions such as Cambridge University, University of Tokyo, Seoul National University, and research centers including Perimeter Institute. Outside research, he participates in outreach and advanced graduate training programs run by entities like Clay Mathematics Institute and Banff International Research Station.
- Pestun, "Localization of gauge theory on a four-sphere and supersymmetric Wilson loops", Journal article, addressing connections to Nekrasov partition function, instanton moduli space, and Seiberg–Witten theory. - Pestun and collaborators, articles on matrix models, relations to AGT correspondence, and extensions to three-dimensional theories published with coauthors from Harvard University and Princeton University. - Reviews and lecture notes authored for workshops at Mathematical Sciences Research Institute and summer schools at Institute for Advanced Study introducing localization techniques and applications to Geometric Langlands program.