Albert S. Schwarz is a mathematician and a theoretical physicist educated in Soviet Union and now a Professor at the University of California

University of California

The University of California is a public university system in the U.S. state of California. Under the California Master Plan for Higher Education, the University of California is a part of the state's three-tier public higher education system, which also includes the California State University...

-Davis. He is one of the pioneers of Morse theory

Morse theory

In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a differentiable function on a manifold will, in a typical case, reflect...

 and brought up the first example of a topological quantum field theory

Topological quantum field theory

A topological quantum field theory is a quantum field theory which computes topological invariants....

. Schwarz worked on some examples in noncommutative geometry

Noncommutative geometry

Noncommutative geometry is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative algebras of functions...

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

Maxim Kontsevich

Maxim Lvovich Kontsevich is a Russian mathematician. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami...

, Schwarz, and Oleg Zaboronsky).

In 1990 Schwarz was an invited speaker of the International Congress of Mathematicians

International Congress of Mathematicians

The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....

 in Kyoto

Kyoto

is a city in the central part of the island of Honshū, Japan. It has a population close to 1.5 million. Formerly the imperial capital of Japan, it is now the capital of Kyoto Prefecture, as well as a major part of the Osaka-Kobe-Kyoto metropolitan area.-History:...

.

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. 400 pp.)
• A. S. Švarc, Математические основы квантовой теории поля, (Mathematical aspects of quantum field theory), Atomizdat, Moscow, 1975. 368 pp.

Papers (selection)

• Albert Schwarz, Oleg 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. A 12(7):1405–1429, 1997
• V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, Phys. Lett. B 257 (1991), no. 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. B 59 (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