Albert S. Black

Albert S. Schwarz or Albert Solomonowitsch Schwarz or Albert Solomonowitsch Schwarts (born June 24, 1934 in Kazan , then Soviet Union ) is a Russian-American mathematician and mathematical physicist.

Life

Schwarz's father disappeared into the Soviet camp system and his mother was also in the camp, so he didn't see her again until 1941. In 1948 they moved from Kazakhstan to Ivanovo . Schwarz attended the Pedagogical Institute in Ivanovo from 1951 (where he studied with WA Yefremovich) and from 1955 the Lomonosov University , where he received his doctorate from Pavel Alexandrov in 1958 (candidate title) and habilitated in 1960 (Russian doctorate). Even as a student, he published papers and, together with Vladimir Boltjanski and Postnikov, organized a seminar on modern methods of topology (however, the seminar announcement was too casual in Alexandrov's eyes and angered him, which had a negative impact on Schwarz's career). The seminar gave important impulses for the algebraic topology in Russia (although there were fewer than 10 participants, including Sergei Novikov ). From 1958 he was assistant professor at the University of Voronezh (with M. Krasnoselski) and from 1961 professor there. From 1964 to 1989 he was professor of theoretical physics at the Moscow Institute of Physics and Technology (MIPT). In 1989 he was a visiting scientist at the ICTP and SISSA in Trieste . In 1990 he became a professor at the University of California, Davis . In the 1990s he was visiting professor at the Institut des Hautes Études Scientifiques (IHES), the Max Planck Institute for Mathematics in Bonn , the Mathematical Sciences Research Institute (MSRI) in Berkeley, Harvard University , the University of California, Berkeley , at CERN , the Isaac Newton Institute in Cambridge , Caltech and the Mittag-Leffler Institute in Stockholm.

Schwarz began as a topologist (including volume invariants of manifolds, topological questions of the calculus of variations, the “gender” of fiber spaces he introduced, the subject of his habilitation), dealt with applications of topology in functional analysis in the 1960s and then turned to the 1970s to mathematical physics (he prefers the term physical mathematics ). First S-matrix theory in quantum field theory , then instantons and magnetic monopoles, which for the first time enabled essential applications of topology in quantum field theory in the 1970s. Schwarz also examined thread-like topological objects in gauge theories, specifically Alice strings in GUTs . The name came from "Alice in Wonderland" by Lewis Carroll , when such strings circulated, a particle in these GUTs could switch to the mirror world that only interacts weakly with the "real world". From the 1980s he dealt with topological quantum field theory (and assumed, independently of Edward Witten, applications in knot theory ), geometry of string theory (multi-loop diagrams, superconforming manifolds and their super -module spaces ), geometry of supergravity , supersymmetric gauge theories, geometry of Batalin-Vilisky quantization Geometry and its application in string theory.

In 1990 he was invited speaker at the International Congress of Mathematicians (ICM) in Kyōto ( Geometry of fermionic string ).

Among his students are Dmitry Fuchs , V. Fateev (Fateev), J. Tyupkin (Tyupkin), I. Frolow.

Fonts

• Gauge theory and topology. Springer, 1993.
• Topology for physicists. Springer, 1996.

See also

• Švarc-Milnor theorem

Web links

• Literature by and about Albert S. Schwarz in the catalog of the German National Library
• Albert S. Schwarz in the Mathematics Genealogy Project (English)
• Albert S. Schwarz at math.ucdavis.edu

Notes and individual references

1. ↑ As the son of an "enemy of the people" (and a Jew), he was initially unable to attend Lomonossow University; after Stalin's death the rules relaxed.
2. ↑ among others with Wladimir Abramowitsch Rochlin on the combinatorial invariance of rational Pontryagin classes, which René Thom also independently proved
3. ^ Tikhomirov: Moscow Mathematics. in Jean-Paul Pier: Development of Mathematics 1950-2000. Birkhäuser, p. 1119
4. ↑ so about the topology of the space of closed curves on a manifold, later of importance in string theory
5. ↑ later rediscovered by Stephen Smale in his complexity studies on real analysis
6. ↑ especially in the work with Alexander Belawin , Alexander Poljakow , J. Tjupkin Pseudoparticle solutions of the Yang-Mills equations . In: Physics Letters B . Volume 59, 1975, p. 85. Schwarz also calculated the dimension of the module space of the instantons.