Alan Weinstein

Summary

Alan David Weinstein (17 June 1943, New York City)[1] is a professor of mathematics at the University of California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry.

Alan Weinstein
AlanWeinsteinbyMargoWeinstein.jpg
BornJune 17, 1943 (1943-06-17) (age 78)
NationalityAmerican
Alma materUniversity of California, Berkeley
Known forMarsden-Weinstein quotient

Weinstein conjecture
Symplectic groupoid

Symplectic category
AwardsSloan Research Fellowship, 1971
Guggenheim Fellowship, 1985
Scientific career
FieldsMathematics
ThesisThe Cut Locus and Conjugate Locus of a Riemannian Manifold (1967)
Doctoral advisorShiing-Shen Chern
Doctoral studentsTheodore Courant
Viktor Ginzburg
Steve Omohundro
Steven Zelditch
Oh Yong-Geun

Education and careerEdit

Weinstein obtained a bachelor's degree at the Massachusetts Institute of Technology in 1964. He received a PhD at University of California, Berkeley in 1967 under the direction of Shiing-Shen Chern. His dissertation was entitled "The cut locus and conjugate locus of a Riemannian manifold".[2]

He worked then at MIT on 1967 (as Moore instructor) and at Bonn University in 1968/69. In 1969 he became assistant professor at Berkeley, and from 1976 he is full professor. During 1978/79 he was visiting professor at Rice University.

Weinstein was awarded in 1971 a Sloan Research Fellowship[3] and in 1985 a Guggenheim Fellowship.[4] In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki.[5] In 1992 he was elected Fellow of the American Academy of Arts and Sciences[6] and in 2012 Fellow of the American Mathematical Society.[7]

ResearchEdit

Weinstein's works cover many areas in differential geometry and mathematical physics, including symplectic geometry, Lie groupoids, geometric mechanics and deformation quantization.

Among his most important contributions, in 1971 he proved a tubular neighbourhood theorem for Lagrangians in symplectic manifolds.[8]

In 1974 he worked with Jerrold Marsden on the theory of reduction for mechanical systems with symmetries, introducing the famous Marsden–Weinstein quotient.[9]

In 1978 he formulated a celebrated conjecture on the existence of periodic orbits,[10] which has been later proved in several particular cases and has led to many new developments in symplectic and contact geometry.[11]

Building on the work of André Lichnerowicz, in a 1983 foundational paper[12] Weinstein proved many results which laid the ground for the development of modern Poisson geometry. A further influential idea in this field was its introduction of symplectic groupoids.[13][14]

He is author of more than 50 research papers in peer-reviewed journals and he has supervised 34 PhD students.[2]

BooksEdit

  • Geometric Models for Noncommutative Algebras (with A. Cannas da Silva), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1999)[15]
  • Lectures on the Geometry of Quantization (with S. Bates), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1997)[16]
  • Basic Multivariable Calculus (with J.E. Marsden and A.J. Tromba), W.A. Freeman and Company, Springer-Verlag (1993), ISBN 978-0-387-97976-2
  • Calculus, I, II, III (with J.E. Marsden), 2nd ed., Springer-Verlag (1985), now out of print and free at CaltechAUTHORS.[17][18][19]
  • Calculus Unlimited (with J.E. Marsden), Benjamin/Cummings (1981), now out of print and free at CaltechAUTHORS.[20]

NotesEdit

  1. ^ American Men and Women of Science, Thomson Gale, 2005
  2. ^ a b "Alan Weinstein - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved 2021-07-17.
  3. ^ "Past Fellows | Alfred P. Sloan Foundation". sloan.org. Retrieved 2021-07-17.
  4. ^ "John Simon Guggenheim Foundation | Alan David Weinstein". Retrieved 2021-07-17.
  5. ^ Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Vol. 2. Helsinki. p. 803.
  6. ^ "Alan David Weinstein". American Academy of Arts & Sciences. Retrieved 2021-07-17.
  7. ^ List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
  8. ^ Weinstein, Alan (1971-06-01). "Symplectic manifolds and their lagrangian submanifolds". Advances in Mathematics. 6 (3): 329–346. doi:10.1016/0001-8708(71)90020-X. ISSN 0001-8708.
  9. ^ Marsden, Jerrold; Weinstein, Alan (1974-02-01). "Reduction of symplectic manifolds with symmetry". Reports on Mathematical Physics. 5 (1): 121–130. Bibcode:1974RpMP....5..121M. doi:10.1016/0034-4877(74)90021-4. ISSN 0034-4877.
  10. ^ Weinstein, Alan (1979-09-01). "On the hypotheses of Rabinowitz' periodic orbit theorems". Journal of Differential Equations. 33 (3): 353–358. Bibcode:1979JDE....33..353W. doi:10.1016/0022-0396(79)90070-6. ISSN 0022-0396.
  11. ^ Pasquotto, Federica (2012-09-01). "A Short History of the Weinstein Conjecture". Jahresbericht der Deutschen Mathematiker-Vereinigung. 114 (3): 119–130. doi:10.1365/s13291-012-0051-1. ISSN 1869-7135. S2CID 120567013.
  12. ^ Weinstein, Alan (1983-01-01). "The local structure of Poisson manifolds". Journal of Differential Geometry. 18 (3). doi:10.4310/jdg/1214437787. ISSN 0022-040X.
  13. ^ Weinstein, Alan (1987). "Symplectic groupoids and Poisson manifolds". Bulletin of the American Mathematical Society. 16 (1): 101–104. doi:10.1090/S0273-0979-1987-15473-5. ISSN 0273-0979.
  14. ^ Coste, A.; Dazord, P.; Weinstein, A. (1987). "Groupoïdes symplectiques". Publications du Département de mathématiques (Lyon) (in French) (2A): 1–62.
  15. ^ "Geometric Models for Noncommutative Algebras". bookstore.ams.org. Retrieved 2021-07-17.
  16. ^ "Lectures on the Geometry of Quantization". bookstore.ams.org. Retrieved 2021-07-17.
  17. ^ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus I.
  18. ^ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus II.
  19. ^ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus III.
  20. ^ Marsden, Jerrold; Weinstein, Alan J. (1981). Calculus Unlimited.

External linksEdit

Further readingEdit

  • The breadth of symplectic and Poisson geometry: festschrift in honor of Alan Weinstein