Murray Gerstenhaber

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Murray Gerstenhaber (born June 5, 1927 in Brooklyn ) is an American mathematician who studied algebra .

Murray Gerstenhaber, Oberwolfach 2010

life and work

Gerstenhaber was gifted at an early age and went to the Bronx High School of Science from 1940 . After serving in the infantry from 1945 to 1947 , he went to Yale University , where he received his bachelor's degree in mathematics in 1948 . In 1947 he won second prize in the William Lowell Putnam competition with the Yale team (in which Murray Gell was also a man ). In 1949 he obtained his master’s degree from the University of Chicago and received his doctorate there in 1951 under Abraham Adrian Albert ( Rings of Derivations ). As a post-doctoral student he was a Frank D. Jewett Fellow at Harvard University in 1951/52 and at the Institute for Advanced Study in 1952/53 . Then he was at the University of Pennsylvania , first from 1953 as an assistant professor , from 1958 as an associate professor and from 1961 as a professor. 1982/83 he was chairman of the faculty senate of the university. He was several times at the Institute for Advanced Study (1952 to 1953, 1957 to 1959, 1962, 1965/66, 1981/82) and 1961/62 at the Institute for Defense Analyzes . In 1990 he was a guest speaker at the inauguration of the Euler Institute in Saint Petersburg .

He dealt with algebraic deformation theory, which he founded in the 1960s. In 1963 he introduced Gerstenhaber algebras as an algebraic structure (with a graded commutative product and a graded Lie algebra) on the Hochschild cohomology , which describes the deformation of algebras. They later found applications, for example, in quantum field theory (Batalin-Vilkovisky formalism in gauge theories) and deformation quantization (including Moshé Flato , Daniel Sternheimer ) in the transition from classical physics to quantum mechanics, and another example of Gerstenhaber algebras is an external product on one Lie algebra. He also dealt with mathematical problems in biology, about which he brought out several anthologies in the 1960s and 1970s.

In addition to his work as a mathematics professor, he received his doctorate in law (JD, Juris Doctor) from the University of Pennsylvania in 1973, was admitted to the Pennsylvania bar in 1974 and has taught at the law school of the University of Pennsylvania. Gerstenhaber also dealt with the application of statistics and probabilistic conclusions in legal questions.

From 1965 to 1971 he was editor of the Bulletin of the American Mathematical Society. He is a fellow of the American Mathematical Society .

He has been married since 1958 and has two sons and a daughter.

Fonts

  • On the deformation of rings and algebras. In: Annals of Mathematics . Volume 79, No. 1, 1964, pp. 59-103, doi : 10.2307 / 1970484 ; Part II: Vol. 84, No. 1, 1966, pp. 1-19, doi : 10.2307 / 1970528 ; Part III: Volume 88, No. 1, 1968, pp. 1-34, doi : 10.2307 / 1970553 ; Part IV: Volume 99, No. 2, 1974, pp. 257-276, doi : 10.2307 / 1970900 ; Part V: with C. Wilkerson in: John McCleary (Ed.): Higher Homotopy Structures in Topology and Mathematical Physics (= Contemporary Mathematics . 227). American Mathematical Society, Providence RI 1999, ISBN 0-8218-0913-X , pp. 89-101.
  • as editor with Michiel Hazewinkel : Deformation theory algebras and structures and applications (= NATO ASI Series. Series C: Mathematical and Physical Sciences. 247). Kluwer, Dordrecht et al. 1988, ISBN 90-277-2804-6 (therein with Samuel D. Schack Algebraic Cohomology and Deformation Theory. Pp. 11-264).
  • as editor with James D. Stasheff : Deformation theory and quantum groups with applications to Mathematical Physics. Proceedings of an AMS-IMS-SIAM 1990 Joint Summer Research Conference held June 14-20 at the University of Massachusetts, Amherst with support from the National Science Foundation (= Contemporary Mathematics. 134). American Mathematical Society, Providence RI 1992, ISBN 0-8218-5141-1 (therein with Samuel D. Schack: Algebras, Bialgebras, Quantum Groups and algebraic deformations. Pp. 51-92).
  • with Philippe Bonneau, Anthony Giaquinto, Daniel Sternheimer Quantum groups and deformation quantization: explicit approaches and implicit aspects. In: Journal of Mathematical Physics . Volume 45, No. 10, 2004, pp. 3703-3741, doi : 10.1063 / 1.1786681 .

literature

  • Alberto S. Cattaneo , Anthony Giaquinto, Ping Xu (Eds.) Higher structures in geometry and physics. In Honor of Murray Gerstenhaber and Jim Stasheff (= Progress in Mathematics. 287). Birkhäuser, New York NY et al. 2011, ISBN 978-0-8176-4734-6 .

Web links

Individual evidence

  1. ↑ Life data according to American Men and Women of Science , Thomson Gale 2004
  2. ^ Curriculum Vitae, accessed from his homepage, January 15, 2012
  3. ↑ Murray Gerstenhaber in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  4. ^ Gerstenhaber: The cohomology structure of an associative ring. In: Annals of Mathematics. Volume 78, No. 2, 1963, pp. 267-288, doi : 10.2307 / 1970343 .
  5. ↑ For example Giaquinto Topics in algebraic deformation theory , in Cattaneo u. a. (Editor) Higher structures in geometry and physics
personal data
SURNAME Barley owner, Murray
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 5, 1927
PLACE OF BIRTH Brooklyn