Alexander A. Voronov Explained

Alexander A. Voronov (Russian: Александр Александрович Воронов) (born November 25, 1962) is a Russian-American mathematician specializing in mathematical physics, algebraic topology, and algebraic geometry. He is currently a Professor of Mathematics at the University of Minnesota and a Visiting Senior Scientist at the Kavli Institute for the Physics and Mathematics of the Universe.^[1]

Biography

Voronov graduated from Moscow State School 57 in 1980. He received an M.S. in Mathematics in 1985 and a Ph.D. in Mathematics at Moscow State University in 1988 under Yuri I. Manin.^[2] Alexander Voronov is known for his work on the super Mumford isomorphism (see Mumford measure), semi-infinite cohomology, operads in quantum field theory (see Swiss-cheese operad), Deligne's and Kontsevich's conjectures on Hochschild cohomology, cohomology of vertex operator algebras, and string topology (see cactus operad). He is a Fellow of the American Mathematical Society, an AMS Centennial Fellow,, a Simons Fellow, and a 2010 Japan Society for the Promotion of Science (JSPS) Research Fellow.

Selected publications

• Voronov. A. A.. A formula for Mumford measure in superstring theory. Russian: [[:ru:Функциональный анализ и его приложения|Functional Anal. Appl.]]. en. 22. 2. 139–140. 1988.
• Rosly. A. A.. Schwarz. A. S.. Voronov. A. A.. Geometry of superconformal manifolds. Comm. Math. Phys.. en. 119. 1. 129–152. 1989. 10.1007/BF01218264. 120761645.
• Voronov. A. A.. Semi-infinite homological algebra. Invent. Math.. en. 113. 1. 103–146. 1993. 10.1007/BF01244304. 1993InMat.113..103V. 122758764.
• Gerstenhaber. M.. Voronov. A. A.. Homotopy G-algebras and moduli space operad. Int. Math. Res. Not.. en. 1995. 3. 141–153. 1995. 10.1155/S1073792895000110. free.
• Kimura. T.. Stasheff. J.. Voronov. A. A.. On operad structures of moduli spaces and string theory. Comm. Math. Phys.. en. 171. 1. 1–25. 1995. 10.1007/BF02103769. hep-th/9307114. 1995CMaPh.171....1K. 17765612.
• Book: Voronov, A. A.. The Swiss-cheese operad. Homotopy invariant algebraic structures (Baltimore, MD, 1998). Contemp. Math.. Providence . AMS . 239. 1999. 365–373.
• Bakalov. B.. Kac. V. G.. Voronov. A. A.. Cohomology of conformal algebras. Comm. Math. Phys.. en. 200. 3. 561–598. 1999. 10.1007/s002200050541. math/9803022. 1999CMaPh.200..561B. 15848034.
• Book: Voronov, A. A.. Homotopy Gerstenhaber algebras. Conférence Moshé Flato 1999, Vol. II (Dijon). Math. Phys. Stud.. Kluwer Academic Publishers . The Netherlands. 22. 2000. 307–331.
• Book: Voronov, A. A.. Notes on universal algebra. Graphs and patterns in mathematics and theoretical physics. Proc. Sympos. Pure Math.. Providence . AMS . 73. 2005. 81–103.
• Hu. P.. Kriz. I.. Voronov. A. A.. On Kontsevich's Hochschild cohomology conjecture. Compositio Mathematica. en. 142. 1. 143–168. 2006. 10.1112/S0010437X05001521. 15153116. math/0309369.
• Book: Hess. K.. Cohen. R. L.. Voronov. A. A.. String topology and cyclic homology. Advanced Courses in Mathematics. CRM Barcelona. Basel . Birkhäuser . 2006. viii+163. 9783764373887. ^[3]

External links

• Alexander Voronov's University of Minnesota web page

Notes and References

1. https://db.ipmu.jp/member/personal/670en.html Kavli IPMU Affiliate member page
2. https://www.genealogy.math.ndsu.nodak.edu/id.php?id=61709&fChrono=1 Mathematics Genealogy Project
3. Latschev, Janko. Review: String topology and cyclic homology by R. L. Cohen, K. Hess, and A. A. Voronov. Bull. Amer. Math. Soc. (N.S.). 2010. 47. 4. 705–712. 10.1090/s0273-0979-09-01265-8. free.