Alan Weinstein
BornJune 17, 1943 (1943-06-17) (age 80)
New York, United States
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

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

After attending Roslyn High School,[2] Weinstein obtained a bachelor's degree at the Massachusetts Institute of Technology in 1964. His teachers included, among others, James Munkres, Gian-Carlo Rota, Irving Segal, and, for the first senior course of differential geometry, Sigurður Helgason.[2]

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".[3]

He worked then at MIT on 1967 (as Moore instructor) and at Bonn University in 1968/69. In 1969 he returned to Berkeley as assistant professor and from 1976 he is full professor. During 1975/76 he visited IHES in Paris[2] and during 1978/79 he was visiting professor at Rice University.

Weinstein was awarded in 1971 a Sloan Research Fellowship[4] and in 1985 a Guggenheim Fellowship.[5] In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki.[6] In 1992 he was elected Fellow of the American Academy of Arts and Sciences[7] and in 2012 Fellow of the American Mathematical Society.[8] In 2003 he was awarded a honorary doctorate from Universiteit Utrecht.[9][10]

Research

Weinstein's works cover many areas in differential geometry and mathematical physics, including Riemannian geometry, symplectic geometry, Lie groupoids, geometric mechanics and deformation quantization.[2][11]

Among his most important contributions, in 1971 he proved a tubular neighbourhood theorem for Lagrangians in symplectic manifolds.[12]

In 1974 he worked with Jerrold Marsden on the theory of reduction for mechanical systems with symmetries, introducing the famous Marsden–Weinstein quotient.[13]

In 1978 he formulated a celebrated conjecture on the existence of periodic orbits,[14] which has been later proved in several particular cases and has led to many new developments in symplectic and contact geometry.[15]

In 1981 he formulated a general principle, called symplectic creed, stating that "everything is a Lagrangian submanifold".[16] Such insight has been constantly quoted as the source of inspiration for many results in symplectic geometry.[2][11]

Building on the work of André Lichnerowicz, in a 1983 foundational paper[17] 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.[18][19]

He is author of more than 50 research papers in peer-reviewed journals and he has supervised 34 PhD students.[3]

Books

  • Geometric Models for Noncommutative Algebras (with A. Cannas da Silva), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1999)[20]
  • Lectures on the Geometry of Quantization (with S. Bates), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1997)[21]
  • 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.[22][23][24]
  • Calculus Unlimited (with J.E. Marsden), Benjamin/Cummings (1981), now out of print and free at CaltechAUTHORS.[25]

Notes

  1. ↑ American Men and Women of Science, Thomson Gale, 2005
  2. 1 2 3 4 5 Bursztyn, Henrique; Fernandes, Rui Loja (2023-01-01). "A Conversation with Alan Weinstein". Notices of the American Mathematical Society. 70 (1): 1. doi:10.1090/noti2595. ISSN 0002-9920. S2CID 254776861.
  3. 1 2 "Alan Weinstein - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved 2021-07-17.
  4. ↑ "Past Fellows | Alfred P. Sloan Foundation". sloan.org. Archived from the original on 2018-03-14. Retrieved 2021-07-17.
  5. ↑ "John Simon Guggenheim Foundation | Alan David Weinstein". Retrieved 2021-07-17.
  6. ↑ Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Vol. 2. Helsinki. p. 803.{{cite book}}: CS1 maint: location missing publisher (link)
  7. ↑ "Alan David Weinstein". American Academy of Arts & Sciences. Retrieved 2021-07-17.
  8. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
  9. ↑ "Archive Honorary Doctorates". Universiteit Utrecht. Retrieved 2023-01-28.
  10. ↑ "Honors and Awards" (PDF). Berkeley Mathematics Newsletter. X (1): 10. Fall 2003.
  11. 1 2 Marsden, Jerrold; Ratiu, Tudor, eds. (2005). "Preface". The Breadth of Symplectic and Poisson Geometry - Festschrift in Honor of Alan Weinstein (PDF). Progress in Mathematics. Vol. 232. Birkhäuser. pp. ix–xii. doi:10.1007/b138687. ISBN 978-0-8176-3565-7.
  12. ↑ 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.
  13. ↑ 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.
  14. ↑ 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.
  15. ↑ 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.
  16. ↑ Weinstein, Alan (July 1981). "Symplectic geometry". Bulletin of the American Mathematical Society. 5 (1): 1–13. doi:10.1090/S0273-0979-1981-14911-9 – via Project Euclid.
  17. ↑ 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.
  18. ↑ 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.
  19. ↑ Coste, A.; Dazord, P.; Weinstein, A. (1987). "Groupoïdes symplectiques". Publications du Département de mathématiques (Lyon) (in French) (2A): 1–62.
  20. ↑ "Geometric Models for Noncommutative Algebras". bookstore.ams.org. Retrieved 2021-07-17.
  21. ↑ "Lectures on the Geometry of Quantization". bookstore.ams.org. Retrieved 2021-07-17.
  22. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus I. Springer. ISBN 9780387909745.
  23. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus II. Springer. ISBN 9780387909752.
  24. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus III. Springer. ISBN 9780387909851.
  25. ↑ Marsden, Jerrold; Weinstein, Alan J. (1981). Calculus Unlimited. Benjamin/Cummings Publishing Company. ISBN 9780805369328.

Further reading

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