KNOWPIA
WELCOME TO KNOWPIA

**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 | |
---|---|

Born | June 17, 1943 | (age 78)

Nationality | American |

Alma mater | University of California, Berkeley |

Known for | Marsden-Weinstein quotient Weinstein conjecture |

Awards | Sloan Research Fellowship, 1971 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 Oh Yong-Geun |

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]}

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]}

*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]}

**^***American Men and Women of Science*, Thomson Gale, 2005- ^
^{a}^{b}"Alan Weinstein - The Mathematics Genealogy Project".*www.mathgenealogy.org*. Retrieved 2021-07-17. **^**"Past Fellows | Alfred P. Sloan Foundation".*sloan.org*. Retrieved 2021-07-17.**^**"John Simon Guggenheim Foundation | Alan David Weinstein". Retrieved 2021-07-17.**^**Lehto, Olii, ed. (1980).*Proceedings of the International Congress of Mathematician 1978*(PDF). Vol. 2. Helsinki. p. 803.**^**"Alan David Weinstein".*American Academy of Arts & Sciences*. Retrieved 2021-07-17.**^**List of Fellows of the American Mathematical Society, retrieved 2013-09-01.**^**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.**^**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.**^**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.**^**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.**^**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.**^**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.**^**Coste, A.; Dazord, P.; Weinstein, A. (1987). "Groupoïdes symplectiques".*Publications du Département de mathématiques (Lyon)*(in French) (2A): 1–62.**^**"Geometric Models for Noncommutative Algebras".*bookstore.ams.org*. Retrieved 2021-07-17.**^**"Lectures on the Geometry of Quantization".*bookstore.ams.org*. Retrieved 2021-07-17.**^**Marsden, Jerrold E.; Weinstein, Alan J. (1985).*Calculus I*.**^**Marsden, Jerrold E.; Weinstein, Alan J. (1985).*Calculus II*.**^**Marsden, Jerrold E.; Weinstein, Alan J. (1985).*Calculus III*.**^**Marsden, Jerrold; Weinstein, Alan J. (1981).*Calculus Unlimited*.

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

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