Biography:Alexander Razborov
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Short description: Russian mathematician
Alexander Razborov | |
|---|---|
| Born | February 16, 1963 Belovo, Russian SFSR, Soviet Union |
| Nationality | American, Russian |
| Alma mater | Moscow State University |
| Known for | group theory, logic in computer science, theoretical computer science |
| Awards |
|
| Scientific career | |
| Fields | Mathematician |
| Institutions | University of Chicago, Steklov Mathematical Institute, Toyota Technological Institute at Chicago |
| Doctoral advisor | Sergei Adian |
Aleksandr Aleksandrovich Razborov (Russian: Алекса́ндр Алекса́ндрович Разбо́ров; born February 16, 1963), sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist. He is Andrew McLeish Distinguished Service Professor at the University of Chicago.
Research
In his best known work, joint with Steven Rudich, he introduced the notion of natural proofs, a class of strategies used to prove fundamental lower bounds in computational complexity. In particular, Razborov and Rudich showed that, under the assumption that certain kinds of one-way functions exist, such proofs cannot give a resolution of the P = NP problem, so new techniques will be required in order to solve this question.
Awards
- Nevanlinna Prize (1990) for introducing the "approximation method" in proving Boolean circuit lower bounds of some essential algorithmic problems,[1]
- Erdős Lecturer, Hebrew University of Jerusalem, 1998.
- Corresponding member of the Russian Academy of Sciences (2000)[2][3]
- Gödel Prize (2007, with Steven Rudich) for the paper "Natural Proofs."[4][5]
- David P. Robbins Prize for the paper "On the minimal density of triangles in graphs" (Combinatorics, Probability and Computing 17 (2008), no. 4, 603–618), and for introducing a new powerful method, flag algebras, to solve problems in extremal combinatorics
- Gödel Lecturer (2010) with the lecture titled Complexity of Propositional Proofs.[6]
- Andrew MacLeish Distinguished Service Professor (2008) in the Department of Computer Science, University of Chicago.
- Fellow of the American Academy of Arts and Sciences (AAAS) (2020).[7]
Bibliography
- Razborov, A. A. (1985). "Lower bounds for the monotone complexity of some Boolean functions". Soviet Mathematics - Doklady 31: 354–357. http://www.mi.ras.ru/~razborov/clique.pdf.
- Razborov, A. A. (June 1985). "Lower bounds on monotone complexity of the logical permanent". Mathematical Notes of the Academy of Sciences of the USSR 37 (6): 485–493. doi:10.1007/BF01157687.
- Разборов, Александр Александрович (1987) (in ru). Московский государственный университет. http://www.mi.ras.ru/~razborov/phd.pdf. (PhD thesis. 32.56MB)
- Razborov, A. A. (April 1987). "Lower bounds on the size of bounded depth circuits over a complete basis with logical addition". Mathematical Notes of the Academy of Sciences of the USSR 41 (4): 333–338. doi:10.1007/BF01137685.
- Razborov, Alexander A. (May 1989). "Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89". Seattle, Washington (state) , United States. pp. 167–176. doi:10.1145/73007.73023. ISBN 0897913078.
- Razborov, A. A. (December 1990). "Lower bounds of the complexity of symmetric boolean functions of contact-rectifier circuits". Mathematical Notes of the Academy of Sciences of the USSR 48 (6): 1226–1234. doi:10.1007/BF01240265.
- Razborov, Alexander A.; Rudich, Stephen (May 1994). "Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94". Montreal , Quebec, Canada. pp. 204–213. doi:10.1145/195058.195134. ISBN 0897916638.
- Razborov, Alexander A. (December 1998). "Lower Bounds for the Polynomial Calculus" (PostScript). Computational Complexity 7 (4): 291–324. doi:10.1007/s000370050013. http://www.mi.ras.ru/~razborov/polynom.ps.
- Razborov, Alexander A. (January 2003). "Propositional proof complexity" (PostScript). Journal of the ACM 50 (1): 80–82. doi:10.1145/602382.602406. http://www.mi.ras.ru/~razborov/jacm50.ps. (Survey paper for JACM's 50th anniversary)
See also
- Avi Wigderson
- Circuit complexity
- Free group
- Natural proofs
- One-way function
- Pseudorandom function family
- Resolution (logic)
Notes
- ↑ "International Mathematical Union: Rolf Nevanlinna Prize Winners". http://mathunion.org/General/Prizes/Nevanlinna/Prizewinners.html.
- ↑ "Russian Academy of Sciences: Razborov Aleksandr Aleksandrovich: General info: History". http://ras.ru/win/db/show_per.asp?P=.id-5681.ln-en.dl-.pr-inf.uk-12.
- ↑ "Russian Genealogy Agencies Tree: R" (in ru). http://rodstvo.ru/R/razin.htm#РАЗБОРОВ.
- ↑ "ACM-SIGACT Awards and Prizes: 2007 Gödel Prize". http://sigact.acm.org/prizes/godel/2007.html.
- ↑ "EATCS: Gödel Prize - 2007". http://eatcs.org/activities/awards/goedel2007.html.
- ↑ "Gödel Lecturers – Association for Symbolic Logic" (in en-US). https://aslonline.org/other-information/prizes-and-awards/godel-lecturers/.
- ↑ "AAAS Fellows Elected". Notices of the American Mathematical Society. https://www.ams.org/journals/notices/202007/rnoti-p1051.pdf.
External links
- Alexander Razborov at the Mathematics Genealogy Project.
- Alexander Razborov's Home Page.
- All-Russian Mathematical Portal: Persons: Razborov Alexander Alexandrovich.
- Biography sketch in the Toyota Technological Institute at Chicago.
- Curricula Vitae at the Department of Computer Science, University of Chicago.
- DBLP: Alexander A. Razborov.
- MathSciNet: "Items authored by Razborov, A. A."[yes|permanent dead link|dead link}}]
- The Work of A.A. Razborov – an article by László Lovász in the Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990.
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