| 词条 | Draft:Serguei Barannikov |
| 释义 |
| name = Serguei Barannikov | birth_date = {{birth date and age|1972|04|16|mf=y}} | birth_place = Moscow,USSR | field = Mathematics | work_institutions ={{Nowrap|Ecole Normale Supérieure Paris Diderot University}} | alma_mater ={{Nowrap|Moscow State University Berkeley University (PhD)}} | academic_advisors = Vladimir Arnold | doctoral_advisor = Maxim Kontsevich[1] }} Serguei Barannikov ({{lang-ru|Сергей Александрович Баранников}}; born April 16, 1972) is a mathematician, known for his works in algebraic topology, algebraic geometry and mathematical physics. Graduated with honors from Moscow State University. At the age of 20 he wrote a paper «Framed Morse complexes and its invariants»[2], where he introduced an important concept in theory of smooth functions and algebraic topology: new invariants of filtered complexes, "canonical forms" or so called Barannikov modules[3][4]. 10 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]. In 1995-1999 Serguei Barannikov received Ph.D in Mathematics from Berkeley University. Simultaneously, he was an invited researcher at Institut des Hautes Etudes Scientifiques in France. From 1999 to 2010 he worked as a researcher at Ecole Normale Supérieure in Paris. From 2010 he works as a researcher at Paris Diderot University. Serguei 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. He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds. In the theory of exponential integrals he is a coauthor of the theorem on the degeneration of analogue of Hodge-de Rham spectral sequence. Known for: Barannikov-Morse complexes[3], Barannikov modules[4], Barannikov-Kontsevich construction[6], Barannikov-Kontsevich theorem[7] References1. ^{{MathGenealogy |id=38692}}} Category:University_of_California,_Berkeley_alumniCategory:Moscow State University alumniCategory:Russian mathematiciansCategory:21st-century mathematiciansCategory:20th-century mathematicians{{authority control}}2. ^{{Cite journal|title = Framed Morse complex and its invariants |url = https://www.researchgate.net/publication/267672645_The_Framed_Morse_complex_and_its_invariants |journal = Advances in Soviet Mathematics |pages = 93–115|volume = 21 (1994)|first = S.|last = Barannikov}} 3. ^1 {{Cite journal|title = Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex|url = https://link.springer.com/article/10.1007/s00023-012-0193-9|journal = Annales Henri Poincaré|pages = 567–610|volume = 14|first = D.|last =Le Peutrec|first2 = N.|last2 = Nier|first3 = C.|last3 = Viterbo}} 4. ^1 2 {{Cite web|url= https://arxiv.org/pdf/1810.03139 |title=F. Le Roux, S.Seyfaddini, C.Viterbo "Barcodes and area-preserving homeomorphisms" |publisher=arxiv.org |accessdate=2019-02-20}} 5. ^{{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}} 6. ^{{Cite web|url=https://arxiv.org/abs/math/9801006 |title= Yu. I. Manin "Three constructions of Frobenius manifolds: a comparative study" |publisher=arxiv.org |accessdate=2019-02-20}} 7. ^{{Cite web|url=https://arxiv.org/pdf/math/0507476.pdf |title= A. Ogus and V. Vologodsky "Nonabelian Hodge Theory in Characteristic p", pages 8,120 |publisher=arxiv.org |accessdate=2019-02-20}} |
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