Serguei Barannikov (Russian: Сергей Александрович Баранников; born April 16, 1972) is a mathematician, known for his works in algebraic topology, algebraic geometry and mathematical physics.
Serguei Barannikov | |
|---|---|
| Born | April 16, 1972 |
| Alma mater | Moscow State University University of California, Berkeley (PhD) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Ecole Normale Supérieure Paris Diderot University |
| Doctoral advisor | Maxim Kontsevich[1] |
| Other academic advisors | Vladimir Arnold |
Biography
editBarannikov graduated with honors from Moscow State University in 1994.
In 1995–1999, Barannikov received his Doctor of Philosophy degree (Ph.D.) in Mathematics from the University of California, Berkeley. Simultaneously, he was an invited researcher at Institut des Hautes Etudes Scientifiques in France.
During 1999–2010, he worked as a researcher at Ecole Normale Supérieure in Paris. Since 2010, he works as a researcher at Paris Diderot University.
Scientific work
editAt the age of 20, Barannikov wrote a paper[2] on algebraic topology, in which he introduced the "canonical forms" invariants of filtered complexes, later also called "Barannikov modules".[3][4] Ten years later, these invariants became widely used in applied mathematics in the field of topological data analysis under the name of "persistence bar-codes" and "persistence diagrams".[4][5]
Barannikov is known for his work on mirror symmetry, Morse theory, and Hodge theory. In mirror symmetry, he is a co-author of construction of Frobenius manifold, mirror symmetric to genus zero Gromov–Witten invariants.[6]
He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds.[7] In the theory of exponential integrals, Barannikov is a co-author of the theorem on the degeneration of analogue of Hodge–de Rham spectral sequence.[8]
In the theory of noncommutative varieties, Barannikov is the author of the theory of noncommutative Hodge structures.[9]
Barannikov is known for: Barannikov–Morse complexes,[3] Barannikov modules,[4] Barannikov–Kontsevich construction,[6] and Barannikov–Kontsevich theorem.[8]
References
edit- ^ Serguei Barannikov at the Mathematics Genealogy Project
- ^ Barannikov, S. (1994). "Framed Morse complex and its invariants". Advances in Soviet Mathematics. ADVSOV. 21: 93–115. doi:10.1090/advsov/021/03. ISBN 9780821802373. S2CID 125829976.
- ^ a b Le Peutrec, D.; Nier, N.; Viterbo, C. (2013). "Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex". Annales Henri Poincaré. 14 (3): 567–610. arXiv:1105.6007. Bibcode:2013AnHP...14..567L. doi:10.1007/s00023-012-0193-9. S2CID 253601705.
- ^ a b c Le Roux, Frédéric; Seyfaddini, Sobhan; Viterbo, Claude (2021). "Barcodes and area-preserving homeomorphisms". Geometry & Topology. 25 (6): 2713–2825. arXiv:1810.03139. doi:10.2140/gt.2021.25.2713. S2CID 119133707.
- ^ "UC Berkeley Mathematics Department Colloquium: Persistent homology and applications from PDE to symplectic topology". events.berkeley.edu. Archived from the original on 2021-04-18. Retrieved 2022-12-16.
- ^ a b Manin, Yu.I. (2002). "Three constructions of Frobenius manifolds: a comparative study". Surveys in Differential Geometry. 7: 497–554. arXiv:math/9801006. doi:10.4310/SDG.2002.v7.n1.a16. S2CID 15448492.
- ^ Seidel, P. (2001). "Vanishing Cycles and Mutation". In Casacuberta C.; Miró-Roig R.M.; Verdera J.; Xambó-Descamps S. (eds.). European Congress of Mathematics. Progress in Mathematics. Vol. 202. Birkhäuser. pp. 65–85. arXiv:math/0007115. doi:10.1007/978-3-0348-8266-8_7. ISBN 978-3-0348-8266-8. S2CID 2347878.
- ^ a b Ogus, Arthur; Vologodsky, Vadim (2005). "Nonabelian Hodge Theory in Characteristic p". arXiv:math/0507476.
- ^ Katzarkov, L.; Kontsevich, M.; Pantev (2008). "Hodge theoretic aspects of mirror symmetry". In Ron Y. Donagi; Katrin Wendland (eds.). From Hodge theory to integrability and TQFT tt*-geometry. Proceedings of Symposia in Pure Mathematics. Vol. 78. American Mathematical Society. pp. 87–174. arXiv:0806.0107. Bibcode:2008arXiv0806.0107K. ISBN 978-0-8218-4430-4. MR 2483750.