Alan Weinstein | Academic Influence

Alan Weinstein's AcademicInfluence.com Rankings

Alan Weinstein

Mathematics

#283

World Rank

#612

Historical Rank

#135

USA Rank

Measure Theory

#362

World Rank

#539

Historical Rank

#155

USA Rank

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Mathematics

Alan Weinstein's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Alan Weinstein Influential?

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According to Wikipedia, Alan David Weinstein 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, 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.

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Alan Weinstein's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Reduction of symplectic manifolds with symmetry (1974) (1378)
Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential (1986) (926)
Nonlinear stability of fluid and plasma equilibria (1985) (874)
Manin Triples for Lie Bialgebroids (1995) (684)
Local structure of Poisson manifolds (2021) (588)
Symplectic manifolds and their lagrangian submanifolds (1971) (578)
Geometric Models for Noncommutative Algebras (1999) (568)
Poisson Lie groups, dressing transformations, and Bruhat decompositions (1990) (552)
Lectures on Symplectic Manifolds (1977) (543)
Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids (1983) (517)
Poisson Geometry with a 3-Form Background (2001) (448)
Semidirect products and reduction in mechanics (1984) (371)
Normal modes for nonlinear hamiltonian systems (1973) (356)
Symplectic groupoids and Poisson manifolds (1987) (339)
The Hamiltonian structure of the Maxwell-Vlasov equations (1982) (326)
Progress in mathematics (1979) (308)
Contact surgery and symplectic handlebodies (1991) (295)
Coisotropic calculus and Poisson groupoids (1988) (283)
Groupoids: unifying internal and external symmetry (1996) (279)
The modular automorphism group of a Poisson manifold (1997) (272)
Periodic Orbits for Convex Hamiltonian Systems (1978) (265)
On the hypotheses of Rabinowitz' periodic orbit theorems (1979) (243)
Transverse measures, the modular class, and a cohomology pairing for Lie algebroids (1996) (238)
Lectures on the geometry of quantization (1995) (235)
Pseudodifferential operators on differential groupoids (1997) (224)
Asymptotics of eigenvalue clusters for the Laplacian plus a potential (1977) (209)
A universal phase space for particles in Yang-Mills fields (1978) (189)
Courant Algebroids and Strongly Homotopy Lie Algebras (1998) (183)
Integration of twisted Dirac brackets (2003) (172)
Extensions of symplectic groupoids and quantization. (1991) (163)
Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces (2000) (152)
Lagrangian Submanifolds and Hamiltonian Systems (1973) (143)
Review: Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, and Nolan R. Wallach, Symplectic geometry and Fourier analysis (1979) (133)
Reduction and Hamiltonian structures on duals of semidirect product Lie algebras (1984) (128)
Classical solutions of the quantum Yang-Baxter equation (1992) (126)
Hamiltonian systems with symmetry, coadjoint orbits and plasma physics (1983) (120)
Fat bundles and symplectic manifolds (1980) (119)
Lie-Poisson structure on some Poisson Lie groups (1992) (115)
Group systems, groupoids, and moduli spaces of parabolic bundles (1995) (111)
Moments and Reduction for Symplectic Groupoids (1988) (109)
on Deformation Quantization (2000) (89)
Northern California symplectic geometry seminar (1999) (88)
Geometry of the transport equation in multicomponent WKB approximations (1994) (85)
Dirac Structures and Poisson Homogeneous Spaces (1996) (85)
Groupoids: Unifying Internal and External Symmetry A Tour through Some Examples (1996) (84)
Connections of Berry and Hannay type for moving Lagrangian submanifolds (1990) (84)
The symplectic “category” (1982) (80)
Symplectic v‐manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds (1977) (79)
On the volume of manifolds all of whose geodesics are closed (1974) (78)
Bifurcations and Hamilton's principle (1978) (78)
Hochschild cohomology and characteristic classes for star products (1997) (75)
ii Multiplicative and Affine Poisson Structures on Lie Groups (2011) (74)
LINEARIZATION OF REGULAR PROPER GROUPOIDS (2001) (74)
Geometry, Mechanics, and Dynamics (2002) (71)
Courant Algebroids and Strongly and Strongly Homotopy Lie Algebras (1998) (68)
Closed forms on symplectic fibre bundles (1983) (67)
Poisson Geometry (2001) (65)
Nonlinear stability conditions and a priori estimates for barotropic hydrodynamics (1983) (64)
Reduction and quantization for singular momentum mappings (1983) (64)
The cut locus and conjugate locus of a Riemannian manifold (1968) (61)
The rigidity of sine‐gordon breathers (1994) (56)
Groupoid symmetry and constraints in general relativity (2010) (56)
Cohomology of symplectomorphism groups and critical values of hamiltonians (1989) (56)
Comments on: The Maxwell-Vlasov equations as a continuous hamiltonian system (1981) (54)
Hamiltonian structure for drift waves and geostrophic flow (1983) (51)
The symplectic structure on moduli space (1995) (50)
Poisson geometry and Morita equivalence (2004) (48)
Picard groups in Poisson geometry (2003) (47)
Poisson geometry of the principal series and nonlinearizable structures (1987) (44)
The Hamiltonian structure of the BBGKY hierarchy equations (1984) (43)
The Differential Geometry of Fedosov’s Quantization (1993) (42)
On the homotopy type of positively-pinched manifolds (1967) (42)
A symplectic fixed point theorem for complex projective spaces (1985) (41)
Omni-Lie Algebras (1999) (41)
Linearization Problems for Lie Algebroids and Lie Groupoids (1999) (41)
A Symbol Class for Some Schrodinger Equations on R n (1985) (38)
The breadth of symplectic and poisson geometry : Festschrift in honor of Alan Weinstein (2005) (37)
On Maslov’s quantization condition (1975) (37)
Positively curved $n$-manifolds in $R^{n+2}$ (1970) (35)
Symplectic Categories (2009) (34)
PSEUDODIFFERENTIAL OPERATORS ON NON-COMPACT MANIFOLDS AND ANALYSIS ON POLYHEDRAL DOMAINS (2004) (34)
Periodic nonlinear waves on a half-line (1985) (34)
Geometry of the Laplace Operator (1982) (34)
Almost invariant submanifolds for compact group actions (1999) (34)
Poisson Geometry of Discrete Series Orbits, and Momentum Convexity for Noncompact Group Actions (2000) (33)
Omni-Lie Algebras (Microlocal Analysis of the Schrodinger Equation and Related Topics) (2000) (33)
Eigenvalues associated with a closed geodesic (1976) (33)
Symplectic Groupoids, Geometric Quantization, and Irrational Rotation Algebras (1991) (32)
Noncommutative Geometry and Geometric Quantization (1990) (32)
Some Comments on the History, Theory, and Applications of Symplectic Reduction (2001) (31)
Distance spheres in complex projective spaces (1973) (30)
Relative modular classes of Lie algebroids (2005) (28)
Errata and addenda: ``The local structure of Poisson manifolds'' (1985) (28)
Quantization and morita equivalence for constant dirac structures on tori (2003) (28)
Symplectic structures on Banach manifolds (1969) (27)
The Integration Problem for Complex Lie Algebroids (2006) (27)
Finite dimensional lie-poisson approximations to vlasov-poisson equations† (1994) (26)
Modular Classes of Lie Algebroid Morphisms (2007) (26)
Stability of rigid body motion using the energy-Casimir method (1984) (26)
Symplectic Geometry, Groupoids, and Integrable Systems (1991) (25)
Basic Multivariable Calculus (1993) (24)
AFFINE POISSON STRUCTURES (1990) (23)
Neighborhood classification of isotropic embeddings (1981) (23)
The Volume of a Differentiable Stack (2008) (23)
Symplectic microgeometry I: micromorphisms (2009) (23)
Variations on Prequantization (2004) (21)
Semiquantum geometry (1996) (21)
Closed curves on convex hypersurfaces and periods of nonlinear oscillations (1981) (20)
Selective Categories and Linear Canonical Relations (2014) (20)
Symplectic microgeometry II: generating functions (2011) (20)
A Fixed Point Theorem for Positively Curved Manifolds (1968) (20)
A note on the Wehrheim-Woodward category (2010) (20)
The invariance of Poincaré's generating function for canonical transformations (1972) (20)
RIEMANNIAN GEOMETRY DURING THE SECOND HALF OF THE TWENTIETH CENTURY (University Lecture Series 17) (2001) (19)
The geometry and mechanics of crossing over. (1958) (19)
Fixed points of analytic actions of supersoluble Lie groups on compact surfaces (2000) (19)
Poisson geometry and deformation quantization near a strictly pseudoconvex boundary (2007) (18)
The Geometry of Momentum (2002) (18)
On the L4 norm of spherical harmonics (1981) (18)
Classical Theta Functions and Quantum Tori (1993) (18)
The Maslov Gerbe (2003) (18)
Symplectic microgeometry III: monoids (2011) (17)
Hopfish algebras (2005) (16)
A comparison theorem for Hamiltonian vector fields (1970) (15)
Integration of Lie algebroid comorphisms (2012) (15)
1998 Some questions about the index of quantized contact transformations (1998) (15)
Group-like objects in Poisson geometry and algebra (2007) (13)
Perturbation of periodic manifolds of hamiltonian systems (1971) (13)
The order and symbol of a distribution (1978) (13)
Hamiltonian Lie algebroids (2018) (13)
Some questions about the index of quantized contact transformations(Geometric methods in asymptotic analysis) (1997) (13)
Groupoid symmetry and constraints in general relativity. 1: kinematics (2010) (12)
Symplectic geometry, groupoids, and integrable systems : séminaire sud rhodanien de géométrie à Berkeley (1989) (1991) (12)
Hopfish structure and modules over irrational rotation algebras (2006) (11)
Poisson Structures and Their Normal Forms (2005) (11)
A Discrete Theory of Connections on Principal Bundles (2005) (11)
Remarks on curvature and the Euler integrand (1971) (10)
Functions Whose Poisson Brackets Are Constants (1971) (10)
Asymptotic equivariant index of Toeplitz operators and relative index of CR structures (2008) (9)
Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces (2015) (9)
Erratum: ``Periodic nonlinear waves on a half-line'' (1986) (8)
Positively curved deformations of invariant Riemannian metrics (1970) (8)
"Geometry, Mechanics, and Dynamics": Volume In Honor Of The 60Th Birthday Of J. E. Marsden (2011) (8)
Singularities of solutions of some Schrödinger equations on ${\text{R}}^n $ (1982) (8)
Removing intersections of Lagrangian immersions (1983) (7)
Poisson geometry in mathematics and physics : international conference, June 5-9, 2006, Tokyo, Japan (2008) (6)
Categories of (co)isotropic linear relations (2015) (6)
The Maslov cycle as a Legendre singularity and projection of a wavefront set (2012) (6)
Symplectic Geometry and Quantization (1994) (6)
A global invertibility theorem for manifolds with boundary (1985) (6)
EXISTENCE OF MULTI-PEAK SOLUTIONS FOR A CLASS OF QUASILINEAR PROBLEMS IN R N (2011) (5)
Pattern Evocation and Energy-Momentum Integration of the Double Spherical PendulumbyJe (1995) (5)
Plasma in a monopole background does not have a twisted Poisson structure (2019) (5)
Gauge groups and Poisson brackets for interacting particles and fields (1982) (4)
Plasma in monopole background is not twisted Poisson. (2019) (4)
The geometry of Poisson brackets (1987) (4)
Coisotropic Pairs (2014) (3)
Decomposition of (Co)isotropic Relations (2015) (3)
The principal symbol of a distribution (1976) (3)
A Lie-Rinehart algebra in general relativity (2022) (3)
THE POINCARÉ-BIRKHOFF THEOREM IN RANDOM DYNAMICS (2013) (2)
SELF-SIMILARITY OF POISSON STRUCTURES ON TORI (2000) (2)
Linearization of Poisson Structures (2005) (2)
Symplectic microgeometry, IV: Quantization (2020) (2)
Remarks on the Construction of Lie-Yamaguti Algebras from Leibniz Algebras (2011) (2)
A New Concept of Deformation Quantization I. Normal Order Quantization on Cotangent Bundles (2)
Poisson geometry and deformation quantization near a pseudoconvex boundary (2006) (2)
Periodic nonlinear waves on a half-line (1985) (2)
Applications of Integration (1985) (2)
Cotangent Microbundle Category, I (2007) (2)
Symplectic geometry and quantization : two symposia on symplectic geometry and quantization problems, July 1993, Japan (1994) (1)
A symplectic rigidity theorem (1983) (1)
Generalities on Poisson Structures (2005) (1)
Lectures on Poisson geometry : proceedings of the summer school on Poisson geometry : ICTP, Trieste, 2005 (2010) (1)
Variations on the prequantization of Poisson manifolds (2005) (1)
Simple periodic orbits (2008) (1)
A ] 5 J an 2 00 7 Complex roots via real roots and square roots using Routh ’ s stability criterion (2008) (1)
An Alternative Form of the Helmholtz Criterionin the Inverse Problem of Cal ulus of VariationsTheodore Voronov (2009) (0)
Further Techniques and Applications of Integration (1985) (0)
Limits, L’Hôpital’s Rule, and Numerical Methods (1985) (0)
Wavefunction collapse , quantum reality , EPR , Bell ’ s Thm , and all that 1 (1996) (0)
The status of the search for gravitational waves (2009) (0)
Star Products and Deformation Quantization (2017) (0)
LIGO Physics Environmental Monitoring at the 40-meter Prototype (2001) (0)
N ov 2 01 6 Decomposition of ( co ) isotropic relations (2018) (0)
The Berkeley Memorial (2009) (0)
The Maslov cycle as a Legendre singularity and projection of a wavefront set (2013) (0)
Memorial for Robert Hermann (2021) (0)
Derivatives and Limits (1985) (0)
Gradients, Maxima, and Minima (1985) (0)
Existence of nontrivial solutions to perturbed Schrödinger system ∗ (2012) (0)
In Honor of Vladimir Drinfeld’s 50th Birthday (2013) (0)
The Elements of Mechanics (Giovanni Gallavotti) (1984) (0)
Rates of Change and the Chain Rule (1985) (0)
Nambu Structures and Singular Foliations (2005) (0)
J ul 2 00 1 Linearization of Regular Proper Groupoids (2001) (0)
Erratum to "Distance Spheres in Complex Projective Spaces" (1975) (0)
Geometry and Analysis on Manifolds (2015) (0)
Calculus I, Second Edition, Corrected 3rd Printing (1985) (0)
Multiplicative and Quadratic Poisson Structures (2005) (0)
Hamiltonian structure of the Maxwell-Vlasov equations. Interim report (1981) (0)
On finding complex roots of polynomials using the Routh array (2005) (0)
A ug 2 00 5 Relative modular classes of Lie algebroids (2005) (0)
Curves and Surfaces (1985) (0)
Q A ] 2 0 A pr 2 00 6 Hopfish algebras (2008) (0)
Contemporary Mathematics Volume 28 , 1984 REDUCTION AND HAMILTONIAN STRUCTURES ON DUALS OF SEMIDIRECT PRODUCT (0)
A COMPARISON THEOREM FOR HAMILTONIAN (2016) (0)
A Geometric Characterization of Solutions to The Algebraic Riccati Equation 1 Introduction (2006) (0)
Standing and travelling waves for nonlinear wave equations (1987) (0)
Decomposition of (Co)isotropic Relations (2016) (0)
Preface to special issue in honor of Kirill C. H. Mackenzie (2021) (0)
Math 242 -symplectic Geometry Lecture Notes (0)
Book Review: Geometric asymptotics@@@Book Review: Symplectic geometry and Fourier analysis (1979) (0)
Hamiltonian Lie algebroids over Poisson manifolds (2023) (0)
Equations of Plasma Physics (1984) (0)
HAMILTONIAN ACTIONS IN GENERALIZED COMPLEX GEOMETRY (2009) (0)
SG ] 4 J un 2 00 3 Picard groups in Poisson geometry (2008) (0)
Manifolds and Mechanics (Arthur Jones, Alistair Gray, and Robert Hutton) (1988) (0)
(Co)isotropic triples and poset representations (2019) (0)
PART ONE Poisson geometry and Morita equivalence (2005) (0)
Poisson Geometry of the Discrete Series, and Momentum Convexity for Noncompact Group Actions (2000) (0)
Fe b 20 04 Poisson geometry and Morita equivalence (2004) (0)
Generalized Polarized Manifolds Azzouz (2014) (0)
Can you hear the shape of a space or the inner structure of the Earth ? (2017) (0)
After its inception as part of Bernhard Riemann's new function theory, Algebraic Geometry quickly became a central area of nineteenth century (2007) (0)
The symplectic structure on moduli space ( in memory of Andreas Floer ) (2011) (0)
Exponentials and Logarithms (1985) (0)
Erratum to: “Distance spheres in complex projective spaces” (Proc. Amer. Math. Soc. 39 (1973), 649–650) (1975) (0)
The holonomy of a singular foliation (2007) (0)
Calculus III, Second Edition, Corrected 5th Printing (1985) (0)
Theoretical Kinematics (O. Bottema and B. Roth) (1980) (0)
Geometry and Analysis on Manifolds : In Memory of Professor Shoshichi Kobayashi (2015) (0)
Variations on Prequantization by Alan Weinstein and Marco Zambon (2005) (0)
Calculus II, Second Edition, Corrected 6th Printing (1985) (0)
Review of Fundamentals (1985) (0)
Book Review: The Floer Memorial Volume (Progress in Mathematics Vo.133) (MATTHIAS SCHWARZ) (1996) (0)
Remembering Jerry Marsden (1942-2010) (2012) (0)
Basic Methods of Integration (1985) (0)
Graphing and Maximum-Minimum Problems (1985) (0)
A pr 2 00 3 Picard groups in Poisson geometry (2003) (0)
Pairs in Poisson and Presymplectic Vector Spaces ? (2015) (0)

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What Schools Are Affiliated With Alan Weinstein?

Alan Weinstein is affiliated with the following schools:

University of California, Berkeley

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