Boris Feigin

Boris Feigin is a mathematician noted for work in representation theory, mathematical physics, and algebraic geometry. He has contributed to the development of vertex algebras, infinite-dimensional Lie algebras, and connections between conformal field theory and geometric representation theory. His career spans positions in academic institutions, collaborations with prominent mathematicians and physicists, and influential publications.

Early life and education

Feigin was born and raised in the Soviet Union and completed his higher education during a period of intense mathematical activity centered in Moscow and Leningrad. He studied at institutions associated with Moscow State University, Steklov Institute of Mathematics, and interacted with research groups linked to Academy of Sciences of the USSR, Mathematical Institute of the Russian Academy of Sciences, and figures connected to the Keldysh Institute of Applied Mathematics. His doctoral work was situated in the milieu of researchers influenced by Israel Gelfand, Boris Dubrovin, Igor Shafarevich, Victor Kac, and Dmitry Faddeev, among others. Early mentors and collaborators included members of seminars drawing participants from Steklov Institute, Moscow State University, Leningrad State University, and visiting scholars from Paris-Sorbonne University and Institute for Advanced Study.

Academic career

Feigin held appointments and visiting positions at institutions such as Steklov Institute of Mathematics, Independent University of Moscow, University of Cambridge, University of Chicago, Columbia University, and research centers including Institut des Hautes Études Scientifiques, Max Planck Institute for Mathematics, and Mathematical Sciences Research Institute. He collaborated with researchers from Harvard University, Princeton University, Yale University, New York University, University of California, Berkeley, and Stanford University. Feigin participated in programs and conferences organized by European Mathematical Society, American Mathematical Society, International Congress of Mathematicians, Society for Industrial and Applied Mathematics, and numerous workshops at CERN, Simons Foundation, and Kavli Institute for Theoretical Physics. His teaching and mentorship connected him with doctoral students who later took positions at Tel Aviv University, University of Toronto, Rutgers University, and St. Petersburg State University.

Research and contributions

Feigin's research spans representation theory of infinite-dimensional algebras, theory of vertex operator algebras, and interactions between algebraic geometry and conformal field theory. He contributed to the understanding of representations of Virasoro algebra, Kac–Moody algebra, and affine Lie algebra structures, situating these in the context of conformal field theory, string theory, and quantum field theory. His work on semi-infinite cohomology and BRST reduction connected methods from Becchi–Rouet–Stora–Tyutin techniques to structures studied in Kazhdan–Lusztig theory and Langlands program. Feigin collaborated on the development of free field realizations, screening operators, and Wakimoto modules associated with affine Kac–Moody algebra representations, linking to constructions by Victor Kac, Edward Frenkel, Michio Jimbo, Nicolai Reshetikhin, and Igor Frenkel. He explored connections between representation categories and geometric objects such as Grassmannian, Flag variety, moduli space of bundles, and Hitchin system, contributing to bridges with the geometric Langlands correspondence and ideas prevalent in work by Alexander Beilinson, Pierre Deligne, Robert Langlands, and Edward Witten. Feigin's results appear in joint papers with researchers including Edward Frenkel, Dmitry Fuks, Vladimir Drinfeld, Maxim Kontsevich, and Gregory Moore, and relate to conjectures addressed at meetings of Institut Henri Poincaré, Banff International Research Station, and Oberwolfach Research Institute for Mathematics.

Awards and honors

Feigin received recognition through invitations to speak at venues such as the International Congress of Mathematicians and plenary or invited lectures at the European Congress of Mathematics. His work has been acknowledged by memberships and fellowships connected to institutions like the Steklov Institute of Mathematics, Russian Academy of Sciences, Simons Foundation, Clay Mathematics Institute, and awards or grants administered by European Research Council and national science agencies. He has been cited in award contexts alongside mathematicians who received Fields Medal, Abel Prize, and Wolf Prize recognition.

Selected publications

- Feigin, with collaborators, on representations of the Virasoro algebra and related vertex algebras, publications appearing in journals associated with American Mathematical Society and Springer collections. - Papers with Edward Frenkel on Wakimoto modules, affine algebras, and semi-infinite cohomology published in proceedings linked to Institute of Physics and Cambridge University Press. - Works with Vladimir Drinfeld and Alexander Beilinson addressing connections to the geometric Langlands correspondence and moduli of bundles, included in volumes associated with World Scientific and Elsevier. - Collaborative articles with Maxim Kontsevich and Gregory Moore linking algebraic structures to topics in string theory and topological field theory appearing in conference proceedings and lecture note series from International Centre for Theoretical Physics and Les Houches Summer School.

Category:Mathematicians