Albert Solomonovich Schwarz[1] (/ʃwɔːrts/ SHWORTS; Russian: Альберт Соломонович Шварц; born June 24, 1934) is a Soviet and American mathematician and a theoretical physicist educated in the Soviet Union and now a professor at the University of California, Davis.
Early life and education
editSchwarz was born in Kazan, Soviet Union. His parents were arrested in the Stalinist purges in 1937.[2]
Schwarz studied under Vadim Yefremovich at Ivanovo Pedagogical Institute, having been denied admittance to Moscow State University on the grounds that he was the son of "enemies of the people."[3]
Career and later life
editAfter defending his dissertation in 1958, he took a job at Voronezh University. In 1964 he was offered a job at Moscow Engineering Physics Institute.[4] He immigrated to the United States in 1989.[5]
Contributions
editSchwarz is one of the pioneers of Morse theory and brought up the first example of a topological quantum field theory.[6] The Schwarz genus, one of the fundamental notions of topological complexity, is named after him.[7] Schwarz worked on some examples in noncommutative geometry. He is the "S" in the AKSZ model (named after Mikhail Alexandrov, Maxim Kontsevich, Schwarz, and Oleg Zaboronski).[8]
Recognition
editIn 1990, Schwarz was an invited speaker of the International Congress of Mathematicians in Kyoto. He was elected to the 2018 class of fellows of the American Mathematical Society.[9]
Monographs
edit- Topology for physicists, Springer, 1996.
- Quantum field theory and topology, Grundlehren der Math. Wissen. 307, Springer 1993 (translated from Russian original Kvantovaja teorija polja i topologija, Nauka, Moscow, 1989).
- A. S. Švarc, Математические основы квантовой теории поля (Mathematical aspects of quantum field theory), Atomizdat, Moscow, 1975.
- Mathematical Foundations of Quantum Field Theory, 2020.
Papers (selection)
edit- A. S. Švarc, A volume invariant of coverings (in Russian), Doklady Akademii Nauk SSSR, 105 (1955), pp. 32–34.
- A. S. Švarc, Род расслоенного пространства, Докл. АН СССР (The genus of a fiber space (Russian), Doklady Akademii Nauk SSSR 119 (1958), no. 2, 219–222.
- A. Schwarz, O. Zaboronsky, Supersymmetry and localization, Comm. Math. Phys. 183(2) (1997), 463–476.
- M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Modern Phys. A12(7):1405–1429, 1997.
- V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, Phys. Lett. B257 (1991), nos. 3–4, 329–334.
- A. A. Belavin, A. M. Polyakov, A. S. Schwartz, Yu. S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B59 (1975), no. 1, 85–87.
- V. N. Romanov, A. S. Švarc, Anomalies and elliptic operators (Russian), Teoret. Mat. Fiz. 41 (1979), no. 2, 190–204.
- S. N. Dolgikh, A. A. Rosly, A. S. Schwarz, Supermoduli spaces, Comm. Math. Phys. 135 (1990), no. 1, 91–100.
See also
editNotes
edit- ^ Credited as Schwartz in A. A. Belavin et al (1975).
- ^ "My life in science" (PDF). ucdavis.edu. Retrieved 18 May 2023.
- ^ "Albert Schwarz". The Mathematics Genealogy Project. Retrieved 18 May 2023.
- ^ "Knots and Quantum Theory - Ideas | Institute for Advanced Study". 5 August 2011.
- ^ Schwarz, Albert (2020). Mathematical Foundations of Quantum Field Theory. ISBN 978-9813278639.
- ^ "Albert Schwarz in nLab".
- ^ Vassiliev, V. A. (2011). "Topological complexity and Schwarz genus of general real polynomial equation". Moscow Mathematical Journal. 11 (3): 617–625, 632. MR 2894434.
- ^ Cattaneo, Alberto S.; Felder, Giovanni (2001). "On the AKSZ formulation of the Poisson sigma model". Letters in Mathematical Physics. 56 (2): 163–179. doi:10.1023/A:1010963926853. MR 1854134.
- ^ 2018 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2017-11-03
References
edit- Albert Schwarz at the Mathematics Genealogy Project
- Biography at ucdavis.edu
- Шварц Альберт Соломонович // Воронежская энциклопедия : в 2 т. / Гл. ред. М. Д. Карпачёв. — Воронеж : Центр духовного возрождения Чернозёмного края, 2008. — Т. 2 : Н — Я. — 524 с. : ил., карты.