Albert Solomonovich Schwarz (; russian: А. С. 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 The University of California, Davis (UC Davis, UCD, or Davis) is a public land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the University of California system. The institut ...

Early life

Schwarz was born in

Kazan Kazan ( ; rus, Казань, p=kɐˈzanʲ; tt-Cyrl, Казан, ''Qazan'', IPA: ɑzan is the capital and largest city of the Republic of Tatarstan in Russia. The city lies at the confluence of the Volga and the Kazanka rivers, covering a ...

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...

. His parents were arrested in the Stalinist purges in 1937. He has two children: a son, Michael A. Schwarz, and a daughter.

Personal life

He has a son and a daughter.

Education and Career

Schwarz studied under Vadim Yefremovich at Ivanovo Pedagogical Institute, having been denied admittance to

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

on the grounds that he was the son of "

enemies of the people The term enemy of the people or enemy of the nation, is a designation for the political or class opponents of the subgroup in power within a larger group. The term implies that by opposing the ruling subgroup, the "enemies" in question are ac ...

." After defending his dissertation in 1958, he took a job at Voronezh University. In 1964 he was offered a job at

Moscow Engineering Physics Institute National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (russian: Национальный исследовательский ядерный университет "МИФИ" / НИЯУ МИФИ or ) is a technical un ...

. He immigrated to the United States in 1989. Schwarz is one of the pioneers of

Morse theory In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiabl ...

and brought up the first example of a

topological quantum field theory In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathem ...

. The Schwarz genus, one of the fundamental notions of topological complexity, is named after him. Schwarz worked on some examples in

noncommutative geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some ge ...

. He is the "S" in the AKSZ model (named after Mikhail Alexandrov,

Maxim Kontsevich Maxim Lvovich Kontsevich (russian: Макси́м Льво́вич Конце́вич, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques an ...

, Schwarz, and Oleg Zaboronski). In 1990, Schwarz was an invited speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Kyoto Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...

. He was elected to the 2018 class of

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Monographs

* ''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)

* A. S. Švarc, A volume invariant of coverings ,

Doklady Akademii Nauk SSSR The ''Proceedings of the USSR Academy of Sciences'' (russian: Доклады Академии Наук СССР, ''Doklady Akademii Nauk SSSR'' (''DAN SSSR''), french: Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that ...

, 105 (1955), pp. 32–34. * A. S. Švarc, Род расслоенного пространства, ''Докл''. ''АН СССР'' (The genus of a fiber space (Russian),

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.

Notes

References

*
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. {{DEFAULTSORT:Schwarz, Albert 1934 births 20th-century American mathematicians 21st-century American mathematicians Mathematicians from Kazan 21st-century American physicists University of California, Davis faculty Living people American people of Russian-Jewish descent Fellows of the American Mathematical Society Topologists