Alan Weinstein

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Alan Weinstein
AlanWeinsteinbyMargoWeinstein.jpg
BornJune 17, 1943 (1943-06-17) (age 78)
New York, USA
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

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.

Education and career[]

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]

Research[]

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]

Books[]

  • 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]

Notes[]

  1. ^ American Men and Women of Science, Thomson Gale, 2005
  2. ^ Jump up to: 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). 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. 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. 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 links[]

Further reading[]

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