Albert Schwarz
Albert S. Schwarz (* June 24, 1934 in Kazan, then Soviet Union) is a Russian- American mathematician and mathematical physicist.
Life
The father of Black disappeared into the Soviet camp system, and his mother was in the camp, so that he saw her again until 1941. In 1948 they moved from Kazakhstan to Ivanovo. Black visited the Ivanovo Pedagogical Institute in 1951 ( where he studied with Yefremovich WA ), and from 1955 the Moscow State University, where he received his doctorate in 1958 Pavel Alexandrov (Candidate title), and in 1960 his habilitation (Russian doctorate ). Even as a student he published works and organized together with Vladimir Postnikov Boltjanski and a seminar on modern methods of topology ( however, was the seminar announcement in the eyes Alexandrov to sloppy and angry that what a negative impact on the careers of Black had ). From the seminar went (although it had less than 10 participants, but including, but Sergei Novikov ) important impetus for the algebraic topology in Russia. From 1958 he was assistant professor at the University of Voronezh ( with M. Krasnosel'skii ) and from 1961 a professor there. 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 has been a 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, at the Isaac Newton Institute in Cambridge, Caltech and the Mittag-Leffler Institute in Stockholm.
Black began as a topologist (including volume - invariants of manifolds, topological questions of variational calculus, which he introduced "gender" of fiber spaces, the object of his habilitation ), dealt in the 1960s with applications of topology in functional analysis, and then turned in the 1970s, the mathematical physics ( he prefers the term physical mathematics). First, S- matrix theory in quantum field theory, then instantons and magnetic monopoles, which first enabled essential applications of topology in quantum field theory in the 1970s. Black also examined filamentous topological objects in gauge theories, especially Alice strings in GUTs. The name came from "Alice in Wonderland" by Lewis Carroll, with circulation of such strings a particle was able to switch to this GUT 's the only weakly with the "real world " interacting mirror world. From the 1980s he focused on topological quantum field theory (and perceived independently by Edward Witten applications in knot theory ), geometry of string theory (multi- loop diagrams, Super Conformal manifolds and their super moduli spaces ), geometry of the supergravity, supersymmetric gauge theories, Geometry of Batalin - Vilkovisky quantization, noncommutative geometry and its applications in string theory.
In 1990 he was invited speaker at the International Congress of Mathematicians (ICM ) in Kyoto ( Geometry of fermionic string).
Among his students heard Dmitry Fuchs, W. Fatejew ( Fateev ), J. Tjupkin ( Tyupkin ), I. Frolov.
Writings
- Gauge theory and topology. Springer, 1993.
- Topology for physicists. Springer, 1996.