American mathematician (born 1943)
For the American historian, educator, and federal official, see
Allen Weinstein .
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 .
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]
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]
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]
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]
^ American Men and Women of Science , Thomson Gale, 2005
^
a
b
c
d
e 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 .
^
a
b
"Alan Weinstein - The Mathematics Genealogy Project" . www.mathgenealogy.org . Retrieved July 17, 2021 .
^
"Past Fellows | Alfred P. Sloan Foundation" . sloan.org . Archived from
the original on March 14, 2018. Retrieved July 17, 2021 .
^
"John Simon Guggenheim Foundation | Alan David Weinstein" . Retrieved July 17, 2021 .
^
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 )
^
"Alan David Weinstein" . American Academy of Arts & Sciences . Retrieved July 17, 2021 .
^
List of Fellows of the American Mathematical Society , retrieved 2013-09-01.
^
"Archive Honorary Doctorates" .
Universiteit Utrecht . Retrieved January 28, 2023 .
^
"Honors and Awards" (PDF) . Berkeley Mathematics Newsletter . X (1): 10. Fall 2003.
^
a
b
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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 July 17, 2021 .
^
"Lectures on the Geometry of Quantization" . bookstore.ams.org . Retrieved July 17, 2021 .
^ Marsden, Jerrold E.; Weinstein, Alan J. (1985).
Calculus I . Springer.
ISBN
9780387909745 .
^ Marsden, Jerrold E.; Weinstein, Alan J. (1985).
Calculus II . Springer.
ISBN
9780387909752 .
^ Marsden, Jerrold E.; Weinstein, Alan J. (1985).
Calculus III . Springer.
ISBN
9780387909851 .
^ Marsden, Jerrold; Weinstein, Alan J. (1981).
Calculus Unlimited . Benjamin/Cummings Publishing Company.
ISBN
9780805369328 .
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