Serguei Barannikov: Difference between revisions
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== Scientific work == |
== Scientific work == |
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At the age of 20, Barannikov wrote a paper<ref name="FMC">{{Cite journal|last=Barannikov|first=S.|year=1994|title=Framed Morse complex and its invariants|url=https://www.researchgate.net/publication/ |
At the age of 20, Barannikov wrote a paper<ref name="FMC">{{Cite journal|last=Barannikov|first=S.|year=1994|title=Framed Morse complex and its invariants|url=https://www.researchgate.net/publication/267672645|journal=Advances in Soviet Mathematics|volume=21|pages=93–115}}</ref> on algebraic topology, in which he introduced the "canonical forms" invariants of filtered complexes, later also called "Barannikov modules".<ref name="BMcomp">{{Cite journal|last=Le Peutrec|first=D.|last2=Nier|first2=N.|last3=Viterbo|first3=C.|title=Precise Arrhenius Law for ''p''-forms: The Witten Laplacian and Morse–Barannikov Complex|journal=Annales Henri Poincaré|volume=14|issue=3|pages=567–610|doi=10.1007/s00023-012-0193-9|year=2013|bibcode=2013AnHP...14..567L}}</ref><ref name="modB">{{Cite arXiv|title=F. Le Roux, S.Seyfaddini, C.Viterbo "Barcodes and area-preserving homeomorphisms"|publisher=arxiv.org|eprint = 1810.03139|author1 = Frédéric Le Roux|last2 = Seyfaddini|first2 = Sobhan|last3 = Viterbo|first3 = Claude|class = math.SG|year = 2018}}</ref> Ten years later, these invariants became widely used in applied mathematics in the field of [[Topological_data_analysis#Early_history|topological data analysis]] under the name of [[Persistent_homology#Definition|"persistence bar-codes"]] and [[Persistent_homology#Definition|"persistence diagrams"]].<ref name="modB" /><ref name="berkeleyClqvm">{{Cite web|url=https://events.berkeley.edu/?event_ID=121726&date=2018-11-29&tab=academic|title=UC Berkeley Mathematics Department Colloquium: Persistent homology and applications from PDE to symplectic topology|publisher=events.berkeley.edu|accessdate=2019-02-20}}</ref> |
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Barannikov is known for his work on [[Mirror_symmetry_(string_theory)|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.<ref name="cstBK"></ref> |
Barannikov is known for his work on [[Mirror_symmetry_(string_theory)|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.<ref name="cstBK"></ref> |
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He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds <ref name="Congr">{{Cite journal|last=Seidel |first=P. |title=Vanishing Cycles and Mutation |
He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds <ref name="Congr">{{Cite journal|last=Seidel |first=P. |title=Vanishing Cycles and Mutation |at= page 1 | journal=European Congress of Mathematics. Progress in Mathematics Vol.202 |year=2001 | isbn= 978-3-0348-8266-8 |publisher= Birkhäuser |arxiv=math/0007115 |doi=10.1007/978-3-0348-8266-8_7 }} </ref>. 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.<ref name="thBK"></ref> |
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|publisher= Birkhäuser }} </ref>. 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.<ref name="thBK"></ref> |
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In the theory of noncommutative varieties, Barannikov is the author of the theory of noncommutative Hodge structures<ref name="nchodge">{{cite journal |last1=Katzarkov |first1=L. |last2=Kontsevich |first2=M. |last3=Pantev |
In the theory of noncommutative varieties, Barannikov is the author of the theory of noncommutative Hodge structures<ref name="nchodge">{{cite journal |last1=Katzarkov |first1=L. |last2=Kontsevich |first2=M. |last3=Pantev |date=2008 |title= Hodge theoretic aspects of mirror symmetry |at= page 5 |journal= Proceedings of Symposia in Pure Mathematics |volume=78 |arxiv=0806.0107 |bibcode=2008arXiv0806.0107K }} </ref>. |
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Barannikov is known for: Barannikov–Morse complexes,<ref name="BMcomp"></ref> Barannikov modules,<ref name="modB"></ref> Barannikov–Kontsevich construction,<ref name="cstBK">{{Cite journal|last=Manin|first=Yu.I. |
Barannikov is known for: Barannikov–Morse complexes,<ref name="BMcomp"></ref> Barannikov modules,<ref name="modB"></ref> Barannikov–Kontsevich construction,<ref name="cstBK">{{Cite journal|last=Manin|first=Yu.I.|title=Three constructions of Frobenius manifolds: a comparative study |journal=Surveys in Differential Geometry|volume=7 |pages=497–554 |
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|date= 2002}}</ref> and Barannikov–Kontsevich theorem.<ref name="thBK">{{Cite |
|date= 2002|arxiv=math/9801006|doi=10.4310/SDG.2002.v7.n1.a16}}</ref> and Barannikov–Kontsevich theorem.<ref name="thBK">{{Cite arXiv|title= A. Ogus and V. Vologodsky "Nonabelian Hodge Theory in Characteristic p"|at= pages 8,120 |publisher=arxiv.org |eprint = math/0507476|author1 = Frédéric Le Roux|last2 = Seyfaddini|first2 = Sobhan|last3 = Viterbo|first3 = Claude|year = 2005}}</ref> |
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== References == |
== References == |
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Revision as of 00:05, 25 May 2019
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 |
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.
Biography
Barannikov 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
At 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
- ^ Serguei Barannikov at the Mathematics Genealogy Project
- ^ Barannikov, S. (1994). "Framed Morse complex and its invariants". Advances in Soviet Mathematics. 21: 93–115.
- ^ 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. Bibcode:2013AnHP...14..567L. doi:10.1007/s00023-012-0193-9.
- ^ a b c Frédéric Le Roux; Seyfaddini, Sobhan; Viterbo, Claude (2018). "F. Le Roux, S.Seyfaddini, C.Viterbo "Barcodes and area-preserving homeomorphisms"". arXiv:1810.03139 [math.SG].
{{cite arXiv}}: Unknown parameter|publisher=ignored (help) - ^ "UC Berkeley Mathematics Department Colloquium: Persistent homology and applications from PDE to symplectic topology". events.berkeley.edu. Retrieved 2019-02-20.
- ^ 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.
- ^ Seidel, P. (2001). "Vanishing Cycles and Mutation". European Congress of Mathematics. Progress in Mathematics Vol.202. Birkhäuser. page 1. arXiv:math/0007115. doi:10.1007/978-3-0348-8266-8_7. ISBN 978-3-0348-8266-8.
- ^ a b Frédéric Le Roux; Seyfaddini, Sobhan; Viterbo, Claude (2005). "A. Ogus and V. Vologodsky "Nonabelian Hodge Theory in Characteristic p"". pages 8,120. arXiv:math/0507476.
{{cite arXiv}}: Unknown parameter|publisher=ignored (help) - ^ Katzarkov, L.; Kontsevich, M.; Pantev (2008). "Hodge theoretic aspects of mirror symmetry". Proceedings of Symposia in Pure Mathematics. 78. page 5. arXiv:0806.0107. Bibcode:2008arXiv0806.0107K.
