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 ...
in
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),
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 ...
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
*
ADHM construction
In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Constru ...
*
BPST instanton
In theoretical physics, the BPST instanton is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu. S. Tyupkin. It is a classical solution to the equations of motion of SU(2) Yang–Mills the ...
*
Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. Mo ...
*
Chern–Simons theory
*
Schwarz-type TQFTs
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 math ...
*
Švarc–Milnor lemma In the mathematical subject of geometric group theory, the Švarc–Milnor lemma (sometimes also called Milnor–Švarc lemma, with both variants also sometimes spelling Švarc as Schwarz) is a statement which says that a group G, equipped with ...
*
Supermanifold
In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below.
Informal definition
An informal definition is com ...
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