Alan Weinstein

For the American historian, educator, and federal official, see Allen Weinstein.

Alan Weinstein
Born	June 17, 1943 (1943-06-17) (age 81) New York, United States
Alma mater	University of California, Berkeley
Known for	Weinstein conjecture Weinstein's neighbourhood theorem Weinstein's symplectic category Marsden–Weinstein quotient Courant algebroid Symplectic groupoid
Awards	Sloan Research Fellowship (1971) ICM Speaker (1978) Guggenheim Fellowship (1985)
Scientific career
Fields	Mathematics
Thesis	The Cut Locus and Conjugate Locus of a Riemannian Manifold  (1967)
Doctoral advisor	Shiing-Shen Chern
Doctoral students	Theodore Courant Viktor Ginzburg Steve Omohundro Steven Zelditch Yong-Geun Oh

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

Early life and education

Weinstein was born in New York City.[1] 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]

Career

Weinstein 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. Bursztyn, Henrique; Fernandes, Rui Loja (January 1, 2023). "A Conversation with Alan Weinstein". Notices of the American Mathematical Society. 70 (1): 1. doi:10.1090/noti2595. ISSN 0002-9920. S2CID 254776861.
3. "Alan Weinstein - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved July 17, 2021.
4. "Past Fellows | Alfred P. Sloan Foundation". sloan.org. Archived from the original on March 14, 2018. Retrieved July 17, 2021.
5. "John Simon Guggenheim Foundation | Alan David Weinstein". Retrieved July 17, 2021.
6. Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Vol. 2. Helsinki. p. 803.
7. "Alan David Weinstein". American Academy of Arts & Sciences. Retrieved July 17, 2021.
8. List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
9. "Archive Honorary Doctorates". Universiteit Utrecht. Retrieved January 28, 2023.
10. "Honors and Awards" (PDF). Berkeley Mathematics Newsletter. X (1): 10. Fall 2003.
11. 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 (June 1, 1971). "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 (February 1, 1974). "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 (September 1, 1979). "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 (September 1, 2012). "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 (January 1, 1983). "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 July 17, 2021.
21. "Lectures on the Geometry of Quantization". bookstore.ams.org. Retrieved July 17, 2021.
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.

External links

• Weinstein's home page.
• Alain Weinstein at University of California, Berkeley
• Alan Weinstein at the Mathematics Genealogy Project

Further reading

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