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Alexander Razborov
Razborov in Oberwolfach, 2024
Born	(1963-02-16) February 16, 1963 (age 61) 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	Nevanlinna Prize (1990) Gödel Prize (2007) Gödel Lecture (2010) David P. Robbins Prize (2013)
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,
• Erdős Lecturer, Hebrew University of Jerusalem, 1998.
• Corresponding member of the Russian Academy of Sciences (2000)
• Gödel Prize (2007, with Steven Rudich) for the paper "Natural Proofs."
• 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.
• 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).

Bibliography

• Razborov, A. A. (1985). "Lower bounds for the monotone complexity of some Boolean functions" (PDF). Soviet Mathematics - Doklady. 31: 354–357.
• 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. S2CID 120875831.
• Разборов, Александр Александрович (1987). О системах уравнений в свободной группе (PDF) (in Russian). Московский государственный университет. (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. S2CID 121744639.
• Razborov, Alexander A. (May 1989). "Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89". Proceedings of the 21st Annual ACM Symposium on the Theory of Computing. Seattle, Washington, 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. S2CID 120703863.
• Razborov, Alexander A.; Rudich, Stephen (May 1994). "Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94". Proceedings of the 26th Annual ACM Symposium on the Theory of Computing. 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. CiteSeerX 10.1.1.19.2441. doi:10.1007/s000370050013. S2CID 8130114.
• Razborov, Alexander A. (January 2003). "Propositional proof complexity" (PostScript). Journal of the ACM. 50 (1): 80–82. doi:10.1145/602382.602406. S2CID 17351318. (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

1. "International Mathematical Union: Rolf Nevanlinna Prize Winners". Archived from the original on 2007-12-17.
2. "Russian Academy of Sciences: Razborov Aleksandr Aleksandrovich: General info: History".
3. "Russian Genealogy Agencies Tree: R" (in Russian). Archived from the original on 2007-12-21. Retrieved 2008-01-15.
4. "ACM-SIGACT Awards and Prizes: 2007 Gödel Prize".
5. "EATCS: Gödel Prize - 2007". Archived from the original on 2007-12-01.
6. "Gödel Lecturers – Association for Symbolic Logic". Archived from the original on 2021-11-08. Retrieved 2021-11-10.
7. "AAAS Fellows Elected" (PDF). Notices of the American Mathematical Society.

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.
• Alexander Razborov's results at International Mathematical Olympiad
• The Work of A.A. Razborov – an article by László Lovász in the Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990.

• 1963 births
• 20th-century Russian mathematicians
• 21st-century Russian mathematicians
• Gödel Prize laureates
• Nevanlinna Prize laureates
• Living people
• Corresponding Members of the Russian Academy of Sciences
• Moscow State University alumni
• Russian computer scientists
• Soviet computer scientists
• Soviet mathematicians
• Theoretical computer scientists
• International Mathematical Olympiad participants
• Fellows of the American Academy of Arts and Sciences
• Russian scientists