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116:.) In a seminal paper in 2009, Zelditch showed that one can recover the shape of a convex, analytic planar domain with up-down symmetries from its Laplace spectrum. In 2019, with his coauthor, Zelditch showed that ellipses of small eccentricity are spectrally determined amongst all smooth, convex planar domains. Among Zelditch's other research topics are
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Shiffman, Bernard; Wunsch, Jared; Anantharaman, Nalini; Douglas, Michael R.; Hanin, Boris; Hassell, Andrew; Hezari, Hamid; Klevtsov, Semyon; Minicozzi, William P.; Phong, Duong H.; Rubinstein, Yanir A.; Shiffman, Bernard; Sogge, Chris; Spruck, Joel; Strohmaier, Alexander; Sturm, Jacob; Toth, John A.;
124:, Gaussian analytic functions, and random metrics. In a famous paper, Zelditch applied semiclassical methods to complex algebraic geometry with the semiclassical parameter playing the role of the reciprocal power of an
106:, equidistribution of eigenfunctions in billiard geometries, quantum ergodic restriction theorems to separating hypersurfaces). He has also done research on the inverse spectral problem. (This problem is described in
132:. The Tian-Yau-Zelditch theorem in this case gives a complete asymptotic expansion of the Bergman kernel near the diagonal. For example, the Catlin-De Angelo-Quillen theorem easily follows from this.
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Bernard Shiffman: Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles, Communications in Mathematical Physics, Vol. 200, 1999, pp. 661–683
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with Pavel Bleher and B. Shiffman: Universality and scaling of correlations between zeros on complex manifolds, Inventiones mathematicae, vol. 142, 2000, pp. 351–395
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43:(13 September 1953 – 11 September 2022) was an American mathematician, specializing in global analysis, complex geometry, and mathematical physics (
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he was from 1985 to 1989 an assistant
Professor, from 1989 to 1992 an associate professor, and from 1992 to 2010 a professor. In 2010 he moved to
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Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke
Mathematical Journal, Vol. 55, 1987, pp. 919–941
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Selberg trace formulae and equidistribution theorems for closed geodesics and
Laplace eigenfunctions: finite area surfaces
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221:"Szegö kernels and a theorem of Tian." International Mathematics Research Notices, Vol. 1998, no. 6, 1998, 317–331
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Weinkove, Ben; Weinstein, Alan; Wentworth, Richard A.; Yau, Shing-Tung; Zworski, Maciej (November 2023).
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Local and Global
Analysis of Natural Functions, Handbook of Geometric Analysis, Volume 1, 2008
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Recent developments in mathematical quantum chaos, Current
Developments in Mathematics 2009
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From random polynomials to symplectic geometry, Proc. Internat. Congress Math. Phys. 2000
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Eigenfunctions and nodal sets, Surveys in
Differential Geometry, Vol. 18, 2013, 237–308
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Complex zeros of real ergodic eigenfunctions, Invent. Math., Vol. 167, 2007, 419–443,
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He has done research on the spectral and scattering theory of the
Laplace operator on
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Quantum
Ergodicity of C* Dynamical Systems, Comm. Math. Phys., 177, 1996, 507–528
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Random
Geometry, Quantum Gravity and the Kähler Potential, Phys. Lett. 705, 2011
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for research done independently; Zelditch was cited for his research on the
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Reconstruction of singularities of solutions for Schrödinger's equations
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Reconstruction of singularities for solutions of Schrödinger's equation
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and especially the asymptotic and distribution of its eigenfunctions (
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Survey of the inverse spectral problem, surveys in Diff. Geom., 2004
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In 1987/88 he was at MIT and in 1988 a visiting professor at
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his bachelor's degree in mathematics and in 1981 from the
333:"Steve Zelditch, September 13, 1953 - September 11, 2022"
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Eigenfunctions on the Laplacian on a Riemannian Manifold
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Eigenfunctions of the Laplacian on a Riemannian manifold
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Prior to his death, he was on the editorial boards of
211:Ergodicity of eigenfunctions for ergodic billiards
520:UC Berkeley College of Letters and Science alumni
428:MAA Reviews, Mathematical Association of America
394:"Huang and Zelditch Awarded 2013 Bergman Prize"
290:IAS / Park City Lectures on Eigenfunctions 2013
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137:Asymptotics of polynomials and eigenfunctions
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535:Fellows of the American Mathematical Society
459:Notices of the American Mathematical Society
401:Notices of the American Mathematical Society
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150:In 2013, he and Xiaojun Huang shared the
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164:Communications in Mathematical Physics
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505:21st-century American mathematicians
500:20th-century American mathematicians
315:, American Mathematical Society 2017
309:, American Mathematical Society 1992
59:University of California, Berkeley
27:American mathematician (1953–2022)
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109:Can you hear the shape of a drum?
69:. From 1981 to 1985 Zelditch was
530:Johns Hopkins University faculty
525:Northwestern University faculty
444:C.V. with Selected Publications
418:Berg, Michael (10 April 2018).
53:Zelditch received in 1975 from
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452:"In Memory of Steve Zelditch"
379:Mathematics Genealogy Project
201:10.1215/S0012-7094-87-05546-3
173:Journal of Geometric Analysis
145:American Mathematical Society
36:Zelditch in Berkeley in 1986
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407:(4): 411–412. April 2014.
227:10.1155/S107379289800021X
358:"Steven Morris Zelditch"
79:Johns Hopkins University
362:Northwestern University
337:Northwestern University
83:Northwestern University
73:Assistant Professor at
515:Harvard College alumni
41:Steven Morris Zelditch
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250:10.1007/s002220000092
237:10.1007/s002200050544
179:Selected publications
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152:Stefan Bergman Prize
97:Riemannian manifolds
75:Columbia University
424:by Steve Zelditch"
169:Analysis & PDE
104:quantum ergodicity
55:Harvard University
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465:(10): 1667–1683.
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