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| Sergey S. Novikov | |
|---|---|
| Name | Sergey S. Novikov |
| Birth date | 1938 |
| Birth place | Moscow |
| Nationality | Soviet / Russia |
| Fields | Mathematics |
| Institutions | Moscow State University, Steklov Institute of Mathematics, Harvard University |
| Alma mater | Moscow State University |
| Doctoral advisor | Andrei Kolmogorov |
| Known for | Topology, Differential topology, Novikov conjecture |
| Awards | Fields Medal, State Prize of the USSR, Lenin Prize |
Sergey S. Novikov is a Soviet and Russian mathematician renowned for foundational work in Topology, Differential geometry, and Algebraic topology. He made decisive contributions to the classification of manifolds, fixed point theory, and the interaction between topology and physics, influencing research across United States and Europe institutions. His conjectures and theorems stimulated developments in K-theory, Index theory, and the study of Elliptic operators.
Novikov was born in Moscow and educated at Moscow State University, where he studied under Andrei Kolmogorov and interacted with scholars from Steklov Institute of Mathematics and Keldysh Institute of Applied Mathematics. During his student years he was influenced by seminars at Moscow Mathematical Society and contacts with mathematicians from Leningrad such as Israel Gelfand and Lev Pontryagin. Early exposure to the work of Henri Poincaré, John Milnor, René Thom, and William Browder shaped his approach to problems in Cobordism and Homotopy theory.
Novikov held positions at Moscow State University and the Steklov Institute of Mathematics, participating in collaborations with researchers at Institute for Advanced Study, Harvard University, and Princeton University. He lectured internationally at venues including Cambridge University, École Normale Supérieure, University of Chicago, ETH Zurich, and University of Paris. He served on editorial boards for journals associated with American Mathematical Society and Springer Science+Business Media, and was involved with initiatives at Russian Academy of Sciences and the International Mathematical Union.
Novikov formulated the eponymous Novikov conjecture connecting higher signatures of manifolds to K-theory and Group theory, prompting work by researchers such as Mikhail Gromov, Gennady Margulis, John Roe, Shmuel Weinberger, and Paul Baum. He proved results in Cobordism theory that extended ideas of René Thom and Milnor's exotic spheres classification, interacting with developments in Surgery theory by C.T.C. Wall and William Browder. Novikov's work on Adams spectral sequence aspects and the application of Atiyah–Singer index theorem connected him with research of Michael Atiyah, Isadore Singer, Raoul Bott, and Daniel Quillen.
His contributions to Differential topology include insights relevant to Morse theory by Marston Morse, formulations overlapping with Bott periodicity, and analysis that influenced later studies by Mikhail Khovanov and Maxim Kontsevich in topological contexts. Novikov introduced techniques bridging Topology and Mathematical Physics, interfacing with ideas from Victor Ginzburg, Edward Witten, Alexander Belavin, and work on Integrable systems like those studied by Lax pair proponents such as Peter Lax. His investigations into Elliptic operators and spectral flow linked to studies by Barry Simon and Mikhail Lifshits.
Novikov's conjectures and theorems generated progress in Operator algebras and Noncommutative geometry pursued by Alain Connes, with applications informing work by Nigel Higson and John Roe on coarse geometry and assembly maps. Collaborations and intellectual descendants include researchers at University of California, Berkeley, Columbia University, Princeton University, and Stanford University.
Novikov received major recognitions including the Fields Medal and national accolades such as the Lenin Prize and the State Prize of the USSR. He was elected to the Russian Academy of Sciences and received honorary positions at institutions including Harvard University, Cambridge University, and ETH Zurich. His awards intersect with international honors granted to contemporaries like Michael Atiyah, Isadore Singer, John Milnor, and Alexander Grothendieck.
- Monographs and papers addressing Cobordism theory, Homotopy theory, and Index theory published in outlets associated with American Mathematical Society and Springer Science+Business Media. Collaborators and coauthors include figures such as Vladimir Arnold, Igor Shafarevich, Andrei Kirillov, and Ludwig Faddeev. His collected works influenced expositions at International Congress of Mathematicians, where he joined speakers like Jean-Pierre Serre and Serge Lang.
Novikov's legacy persists through conjectures cited by mathematicians at Courant Institute of Mathematical Sciences, Institut des Hautes Études Scientifiques, and Max Planck Institute for Mathematics. His students and collaborators continued research in institutions including Moscow State University, Steklov Institute of Mathematics, University of Bonn, and University of Chicago. The Novikov conjecture remains a central open problem linking research by scholars such as Gennadi Kasparov, Mikhail Gromov, and John Roe, and his influence is acknowledged alongside mathematicians like Alexander Grothendieck, Pierre Deligne, and David Mumford.
Category:Russian mathematicians