Biography:Alan Weinstein

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Short description: American mathematician
Alan Weinstein
AlanWeinsteinbyMargoWeinstein.jpg
BornJune 17, 1943 (1943-06-17) (age 81)
New York City , 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

Notes

  1. ↑ American Men and Women of Science, Thomson Gale, 2005
  2. ↑ 2.0 2.1 2.2 2.3 2.4 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. 
  3. ↑ 3.0 3.1 "Alan Weinstein - The Mathematics Genealogy Project". https://www.mathgenealogy.org/id.php?id=31515. 
  4. ↑ "Past Fellows | Alfred P. Sloan Foundation" (in en). https://sloan.org/past-fellows. 
  5. ↑ "John Simon Guggenheim Foundation | Alan David Weinstein" (in en-US). https://www.gf.org/fellows/all-fellows/alan-david-weinstein/. 
  6. ↑ Lehto, Olii, ed (1980). Proceedings of the International Congress of Mathematician 1978. 2. Helsinki. pp. 803. https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1978.2/ICM1978.2.ocr.pdf. 
  7. ↑ "Alan David Weinstein" (in en). https://www.amacad.org/person/alan-david-weinstein. 
  8. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
  9. ↑ "Archive Honorary Doctorates" (in en). https://www.uu.nl/en/organisation/about-us/tradition-and-history/awards-and-distinctions/honorary-doctorates/archive-honorary-doctorates. 
  10. ↑ "Honors and Awards". Berkeley Mathematics Newsletter X (1): 10. Fall 2003. https://math.berkeley.edu/sites/default/files/pages/Fall03.pdf. 
  11. ↑ 11.0 11.1 Marsden, Jerrold, ed (2005). "Preface" (in en). The Breadth of Symplectic and Poisson Geometry - Festschrift in Honor of Alan Weinstein. Progress in Mathematics. 232. Birkhäuser. pp. ix - xii. doi:10.1007/b138687. ISBN 978-0-8176-3565-7. https://media.hugendubel.de/shop/coverscans/889PDF/8897259_lprob_1.pdf. 
  12. ↑ Weinstein, Alan (1971-06-01). "Symplectic manifolds and their lagrangian submanifolds" (in en). 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" (in en). Reports on Mathematical Physics 5 (1): 121–130. doi:10.1016/0034-4877(74)90021-4. ISSN 0034-4877. Bibcode: 1974RpMP....5..121M. http://www.cds.caltech.edu/~marsden/bib/1974/01-MaWe1974/. 
  14. ↑ Weinstein, Alan (1979-09-01). "On the hypotheses of Rabinowitz' periodic orbit theorems" (in en). Journal of Differential Equations 33 (3): 353–358. doi:10.1016/0022-0396(79)90070-6. ISSN 0022-0396. Bibcode: 1979JDE....33..353W. 
  15. ↑ Pasquotto, Federica (2012-09-01). "A Short History of the Weinstein Conjecture" (in en). Jahresbericht der Deutschen Mathematiker-Vereinigung 114 (3): 119–130. doi:10.1365/s13291-012-0051-1. ISSN 1869-7135. https://doi.org/10.1365/s13291-012-0051-1. 
  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. https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-5/issue-1/Symplectic-geometry/bams/1183548217.full. 
  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" (in en). Bulletin of the American Mathematical Society 16 (1): 101–104. doi:10.1090/S0273-0979-1987-15473-5. ISSN 0273-0979. https://www.ams.org/bull/1987-16-01/S0273-0979-1987-15473-5/. 
  19. ↑ Coste, A.; Dazord, P.; Weinstein, A. (1987). "Groupoïdes symplectiques" (in fr). Publications du Département de mathématiques (Lyon) (2A): 1–62. http://www.numdam.org/item/PDML_1987___2A_1_0/. 
  20. ↑ "Geometric Models for Noncommutative Algebras". https://bookstore.ams.org/bmln-10/. 
  21. ↑ "Lectures on the Geometry of Quantization". https://bookstore.ams.org/bmln-8/. 
  22. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus I. Springer. ISBN 9780387909745. http://resolver.caltech.edu/CaltechBOOK:1985.001. 
  23. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus II. Springer. ISBN 9780387909752. http://resolver.caltech.edu/CaltechBOOK:1985.003. 
  24. ↑ Marsden, Jerrold E.; Weinstein, Alan J. (1985). Calculus III. Springer. ISBN 9780387909851. http://resolver.caltech.edu/CaltechBOOK:1985.005. 
  25. ↑ Marsden, Jerrold; Weinstein, Alan J. (1981). Calculus Unlimited. Benjamin/Cummings Publishing Company. ISBN 9780805369328. http://resolver.caltech.edu/CaltechBOOK:1981.001. 

External links

Further reading



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