Steven Zelditch | Academic Influence

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Steven Zelditch

Mathematics

#2971

World Rank

#4473

Historical Rank

#1132

USA Rank

Complex Analysis

#14

World Rank

#25

Historical Rank

#7

USA Rank

Differential Geometry

#49

World Rank

#58

Historical Rank

#19

USA Rank

Geometry

#97

World Rank

#153

Historical Rank

#23

USA Rank

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Mathematics

Steven Zelditch's Degrees

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

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According to Wikipedia, Steven Morris Zelditch was an American mathematician, specializing in global analysis, complex geometry, and mathematical physics . Zelditch received in 1975 from Harvard University his bachelor's degree in mathematics and in 1981 from the University of California, Berkeley his Ph.D. under Alan Weinstein with thesis Reconstruction of singularities of solutions for Schrödinger's equations. From 1981 to 1985 Zelditch was Ritt Assistant Professor at Columbia University. At Johns Hopkins University 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 Northwestern University, where he was Wayne and Elizabeth Jones Professor of Mathematics.

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Steven Zelditch'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

Szego kernels and a theorem of Tian (2000) (594)
Uniform distribution of eigenfunctions on compact hyperbolic surfaces (1987) (577)
Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles (1998) (255)
Universality and scaling of correlations between zeros on complex manifolds (1999) (195)
Ergodicity of eigenfunctions for ergodic billiards (1996) (188)
EIGENFUNCTIONS AND NODAL SETS (2012) (183)
Riemannian manifolds with maximal eigenfunction growth (2001) (156)
Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: An addendum (2002) (130)
Critical Points and Supersymmetric Vacua I (2004) (127)
Index and dynamics of quantized contact transformations (2000) (120)
Kuznecov sum formulae and Szegö limit formulae on manifolds (1992) (99)
Number Variance of Random Zeros on Complex Manifolds (2006) (92)
Spectral determination of analytic bi-axisymmetric plane domains (2000) (86)
The inverse spectral problem (2004) (85)
Riemannian manifolds with uniformly bounded eigenfunctions (2000) (84)
Counting Nodal Lines Which Touch the Boundary of an Analytic Domain (2007) (81)
Reconstruction of singularities for solutions of Schrödinger's equation (1983) (81)
Quantum Ergodicity of Boundary Values of Eigenfunctions (2002) (80)
Lower bounds on the Hausdorff measure of nodal sets II (2010) (79)
EQUILIBRIUM DISTRIBUTION OF ZEROS OF RANDOM POLYNOMIALS (2002) (77)
Recent Developments in Mathematical Quantum Chaos (2009) (77)
About the Blowup of Quasimodes on Riemannian Manifolds (2009) (69)
Real and complex zeros of Riemannian random waves (2008) (68)
Quantum Ergodic Restriction Theorems: Manifolds Without Boundary (2011) (67)
Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics (2004) (66)
Quantum ergodicity on the sphere (1992) (65)
On the rate of quantum ergodicity I: Upper bounds (1994) (65)
LOCAL AND GLOBAL ANALYSIS OF EIGENFUNCTIONS ON RIEMANNIAN MANIFOLDS (2009) (64)
The inverse spectral problem for surfaces of revolution (2000) (62)
Quantum ergodicity of C * -dynamical systems (1995) (61)
Weyl's law and quantum ergodicity for maps with divided phase space (2004) (54)
Determinants of Laplacians in Exterior Domains (2000) (54)
Inverse spectral problem for analytic domains, II: ℤ2-symmetric domains (2009) (53)
Random polynomials with prescribed Newton polytope (2002) (53)
Pseudo-differential analysis on hyperbolic surfaces (1986) (53)
Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution (2013) (53)
Eigenfunctions of the Laplacian on a Riemannian manifold (2017) (51)
Classical Limits of Eigenfunctions for Some Completely Integrable Systems (1999) (51)
Critical Points and Supersymmetric Vacua, III: String/M Models (2005) (51)
Universality and Scaling of Zeros on Symplectic Manifolds (2000) (50)
Large Deviations of Empirical Measures of Zeros of Random Polynomials (2010) (49)
Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series (1991) (49)
Poincaré–Lelong Approach to Universality and Scaling of Correlations Between Zeros (1999) (48)
Lp Norms of Eigenfunctions in the Completely Integrable Case (2002) (47)
On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature (2011) (45)
Random polynomials of high degree and Levy concentration of measure (2003) (45)
Wave invariants at elliptic closed geodesics (2000) (45)
Quantum transition amplitudes for ergodic and for completely integrable systems (1990) (43)
Complex zeros of real ergodic eigenfunctions (2005) (43)
Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I (2011) (42)
Fine Structure of Zoll Spectra (1997) (42)
Focal points and sup-norms of eigenfunctions (2013) (42)
Gravitational Actions in Two Dimensions and the Mabuchi Functional (2011) (41)
Quantum ergodicity ofC* dynamical systems (2000) (41)
Bergman metrics and geodesics in the space of K (2007) (41)
Test configurations, large deviations and geodesic rays on toric varieties (2007) (41)
C∞ spectral rigidity of the ellipse (2012) (41)
Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers (2003) (40)
Survey of the inverse spectral problem (2004) (40)
The Cauchy problem for the homogeneous Monge-Ampere equation, I. Toeplitz quantization (2010) (40)
Inverse Spectral Problem for Analytic Domains I: Balian-Bloch Trace Formula (2001) (39)
Wave Invariants for Non-degenerate Closed Geodesics (2000) (39)
Patterson–Sullivan Distributions and Quantum Ergodicity (2006) (38)
Quantum Ergodicity and Mixing of Eigenfunctions (2006) (37)
The Cauchy problem for the homogeneous Monge-Ampère equation, II. Legendre transform (2010) (37)
Quantum ergodic restriction for Cauchy data: Interior QUE and restricted QUE (2012) (37)
Overcrowding and hole probabilities for random zeros on complex manifolds (2008) (34)
INVERSE SPECTRAL PROBLEM FOR ANALYTIC DOMAINS II: Z2- SYMMETRIC DOMAINS (2001) (32)
Quantum Ergodic Restriction Theorems. I: Interior Hypersurfaces in Domains with Ergodic Billiards (2010) (32)
A Random Matrix Model for Quantum Mixing (1996) (31)
Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$ (2009) (30)
Maximally degenerate laplacians (1996) (30)
Measure of nodal sets of analytic Steklov eigenfunctions (2014) (29)
Norms of Modes and Quasi-modes revisited (2002) (29)
Distribution laws for integrable eigenfunctions (2003) (29)
Random Kähler metrics (2011) (29)
Spectral statistics on zoll surfaces (1993) (29)
THE MODULUS OF CONTINUITY FOR Γ 0 ( m ) \ H SEMI-CLASSICAL LIMITS (28)
Central limit theorem for spectral partial Bergman kernels (2017) (28)
Bernstein polynomials, Bergman kernels and toric Kähler varieties (2007) (28)
Correlations Between Zeros and Supersymmetry (2000) (25)
Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary (2014) (25)
Note on quantum unique ergodicity (2003) (24)
Concerning the L4 norms of typical eigenfunctions on compact surfaces (2010) (24)
On the generic spectrum of a riemannian cover (1990) (24)
Selberg trace formulae and equidistribution theorems for closed geodesics and Laplace eigenfunctions: finite area surfaces (1992) (24)
Addendum to "Lower bounds on the Hausdorff measure of nodal sets" (2012) (23)
Bergman approximations of harmonic maps into the space of Kahler metrics on toric varieties (2008) (23)
Local and global analysis of eigenfunctions (2009) (23)
Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kähler manifolds (2016) (22)
HARMONIC ANALYSIS ON TORIC VARIETIES (2003) (21)
Convergence of Bergman geodesics on CP^1 (2007) (21)
Large deviations of empirical measures of zeros on Riemann surfaces (2011) (21)
On a “quantum chaos” theorem of R. Schrader and M. Taylor (1992) (21)
Isospectrality in the FIO category (1992) (21)
Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator (2013) (20)
Random geometry, quantum gravity and the Kähler potential (2011) (20)
A Gutzwiller trace formula for stationary space-times (2018) (19)
From Random Polynomials to Symplectic Geometry (2000) (19)
The averaging method and ergodic theory for pseudo-differential operators on compact hyperbolic surfaces (1989) (18)
Ergodicity and intersections of nodal sets and geodesics on real analytic surfaces (2012) (18)
Quantum ergodicity of random orthonormal bases of spaces of high dimension (2012) (18)
One can hear the shape of ellipses of small eccentricity (2019) (17)
Inverse Resonance Problem for ℤ2-Symmetric Analytic Obstacles in the Plane (2004) (17)
Completeness of boundary traces of eigenfunctions (2013) (15)
Trace formula for compact $\Gamma\setminus PSL_{2}(\mathbb{R})$ and the equidistribution theory of closed geodesics (1989) (15)
Logarithmic lower bound on the number of nodal domains (2015) (15)
Macdonald’s Identities and the Large N Limit of YM2 on the Cylinder (2003) (15)
Level Spacings for Integrable Quantum Maps in Genus Zero (1998) (14)
Critical values of random analytic functions on complex manifolds (2012) (14)
Szegő kernels and Poincaré series (2013) (14)
Spectral Theory and Geometry: Lectures on wave invariants (1999) (14)
Number variance of random zeros (2005) (14)
SZEGÖ LIMIT THEOREMS FOR THE HARMONIC OSCILLATOR (1983) (14)
Spacing Between Phase Shifts in a Simple¶Scattering Problem (2000) (13)
Focal points and sup-norms of eigenfunctions II: the two-dimensional case (2016) (13)
Simple matrix models for random Bergman metrics (2011) (13)
A note on $L^p$-norms of quasi-modes (2014) (13)
LARGE DEVIATIONS OF EMPIRICAL ZERO POINT MEASURES ON RIEMANN SURFACES, I: g = 0 (2009) (13)
Inverse Spectral Problem for Analytic $${{(\mathbb{Z}/2 \mathbb{Z})^{n}}}$$ -Symmetric Domains in $${{\mathbb{R}^{n}}}$$ (2010) (12)
The Cauchy problem for the homogeneous Monge–Ampère equation, III. Lifespan (2012) (12)
Stability and integration over Bergman metrics (2014) (12)
On the rate of Quantum Ergodicity, II: Lower bounds (1994) (12)
Quantum Ergodicity and Mixing (2005) (11)
Park City lectures on Eigenfunctions (2013) (11)
Nodal intersections and geometric control (2017) (11)
Random zeros on complex manifolds: conditional expectations (2010) (11)
Median and mean of the Supremum of $L^2$ normalized random holmorphic fields (2013) (11)
Selberg trace formulae, pseudodifferential operators, and geodesic periods of automorphic forms (1988) (10)
Pointwise Weyl laws for Partial Bergman kernels (2013) (10)
The inverse resonance problem for $\Z_2$-symmetric analytic obstacles in the plane (2002) (10)
Equidistribution of phase shifts in semiclassical potential scattering (2013) (9)
Random Complex Fewnomials, I (2010) (9)
Szegö limit theorems in quantum mechanics (1983) (9)
Quantum maps and automorphisms (2003) (8)
Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary (2014) (8)
Interface asymptotics of Partial Bergman kernels around a critical level (2018) (8)
Singularities of solutions of some Schrödinger equations on ${\text{R}}^n $ (1982) (8)
Large Deviations for Zeros of P(ϕ)2 Random Polynomials (2010) (8)
Off-Diagonal Decay of Toric Bergman Kernels (2016) (8)
Inverse spectral problem for analytic plane domains II: $\Z_2$-symmetric domains (2001) (8)
Spectral asymptotics on stationary space-times (2020) (8)
Book Review: Holomorphic Morse inequalities and Bergman kernels (2008) (8)
Semi-classical mass asymptotics on stationary spacetimes (2020) (8)
Billiards and boundary traces of eigenfunctions (2003) (7)
Addendum to "Energies of zeros of random sections on Riemann surfaces" [arXiv:0705.2000]. Indiana Univ. Math. J. 57 (2008), no. 4, 1753-1780 (2010) (7)
Asymptotics of Polynomials and Eigenfunctions (2002) (7)
Quantum ergodicity for Eisenstein functions (2015) (6)
Chapter Eighteen. On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature (2014) (6)
Addendum to "Energies of zeros of random sections on Riemann surfaces" Indiana Univ. Math. J. 57 (2008), no. 4, 1753--1780 (2010) (6)
Gaussian beams on Zoll manifolds and maximally degenerate Laplacians (2014) (6)
On the Spectrum of geometric operators on K (2008) (6)
Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces (2010) (6)
Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza–Klein 3-folds (2018) (6)
Normal form of the wave group and inverse spectral theory (1998) (5)
Asymptotics of almost holomorphic sections on symplectic manifolds (2002) (5)
Quantum Ergodic Restriction Theorems: Manifolds Without Boundary (2013) (5)
Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic (2016) (5)
Geodesics in homology classes and periods of automorphic forms (1991) (4)
Random Riesz energies on compact Kähler manifolds (2011) (4)
Quantum Ergodic Sequences and Equilibrium Measures (2017) (4)
Fourier coefficients of restrictions of eigenfunctions (2020) (4)
Topology of the Nodal Set of Random Equivariant Spherical Harmonics on 𝕊3 (2019) (4)
Scaling asymptotics of heat kernels of line bundles (2014) (4)
Geodesic biangles and Fourier coefficients of restrictions of eigenfunctions (2021) (4)
Mathematics of Quantum Chaos in 2019 (2019) (4)
$C^{\infty} $ spectral rigidity of the ellipse (2010) (3)
Log-Scale Equidistribution of Zeros of Quantum Ergodic Eigensections (2017) (3)
Spectrum and Geodesic Flow (1992) (3)
Local and global analysis of eigenfunctions: Advanced Lectures in Mathematics, Vol. 7 (2008) (3)
Interface asymptotics of eigenspace Wigner distributions for the harmonic oscillator (2019) (3)
A Szegö limit formula for conjugates of ψ DO's by Hecke operators (1988) (3)
Addendum: Level spacings for integrable quantum maps in genus zero 1 (2000) (3)
Heat kernel measures on random surfaces (2015) (3)
Nodal lines, ergodicity and complex numbers (2007) (3)
Focal points and sup-norms of eigenfunctions on analytic Riemannian manifolds II: the two-dimensional case (2014) (3)
RANDOM COMPLEX GEOMETRY AND VACUA, OR: HOW TO COUNT UNIVERSES IN STRING/M THEORY (2005) (3)
Central limit theorem for toric Kähler manifolds (2018) (3)
Matrix elements of Fourier Integral Operators (2013) (2)
Appendix to Kaplan-Heller (1998) (2)
Quantum unique ergodicity (2003) (2)
Spectral determination of analytic axi-symmetric plane domains (1999) (2)
Entropy of Bergman measures of a toric Kaehler manifold (2019) (2)
Quantum Ergodic Restriction Theorems. I: Interior Hypersurfaces in Domains with Ergodic Billiards (2011) (2)
Semi‐classical limit of random walks II (1998) (2)
Semi{classical Limit for Random Walks (2000) (2)
Lower bounds for Cauchy data on curves in a negatively curved surface (2020) (2)
Inverse spectral problem for analytic plane domains II: domains with symmetry (2001) (2)
Counter-example to conjectured SU(N) character asymptotics (2003) (2)
$2$-nodal domain theorems for higher dimensional circle bundles (2022) (1)
Interface asymptotics of Wigner—Weyl distributions for the Harmonic Oscillator (2019) (1)
Eigenfunction asymptotics and spectral rigidity of the ellipse (2020) (1)
Counting String/M Vacua (2006) (1)
Level Spacings for Integrable Quantum Maps in Genus Zero (2000) (1)
Schrödinger trace invariants for homogeneous perturbations of the harmonic oscillator (2018) (1)
Survey of positive results on the inverse spectral problem (2003) (1)
Addendum to: "Critical values of random analytic functions on complex manifolds" (2017) (1)
Spectral determination of analytic bi-axisymmetric plane domains (1999) (1)
Critical values of fixed Morse index of random analytic functions on Riemann surfaces (2015) (1)
RANDOM ALMOST HOLOMORPHIC SECTIONS OF AMPLE LINE BUNDLES ON SYMPLECTIC MANIFOLDS (2000) (1)
Asymptotics of holomorphic sections of powers of a positive line bundle (1998) (1)
Splitting of geodesics in homology classes (1989) (1)
PR ] 9 A ug 2 01 6 HEAT KERNEL MEASURES ON RANDOM SURFACES (2018) (0)
Log-Scale Equidistribution of Zeros of Quantum Ergodic Eigensections (2018) (0)
Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary (2015) (0)
A P ] 2 1 N ov 2 01 8 A GUTZWILLER TRACE FORMULA FOR STATIONARY SPACETIMES (2018) (0)
Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic (2016) (0)
Self-focal points of ellipsoids of dimension $\geq 3$. (2020) (0)
Survey of the inverse spectral problem for the Notices of the ICCM (2015) (0)
Gaussian random polynomials and analytic functions (2006) (0)
Comments on S.-T. Yau (2019) (0)
LECTURES ON GEODESICS IN THE SPACE OF KAEHLER METRICS , LECTURE 3 : HRMA , HCMA AND TORIC KAEHLER MANIFOLDS (2015) (0)
Complex geometry and vacua : Counting universes in string theory (2006) (0)
Nodal lines of Laplace eigenfunctions ” Spectral Analysis in Geometry and Number Theory ” on the occasion of Toshikazu Sunada ’ s 60 th birthday Friday , August 10 , 2007 (0)
Steven Zelditch (2019) (0)
Restriction of eigenfunctions to totally geodesic submanifolds (2022) (0)
Ju n 20 03 DISTRIBUTION LAWS FOR INTEGRABLE EIGENFUNCTIONS (2008) (0)
LECTURES ON GEODESICS IN THE SPACE OF KAEHLER METRICS , LECTURE 4 : QUANTIZATION (2015) (0)
7 Proof of Theorem 3 : Euler-MacLaurin approach 834 8 Interface asymptotics : Proof of Theorem 4 838 9 Distribution of zero locus of a Random section : Proof of Theorem 5 846 10 Example : The Bargmann-Fock model 848 (2019) (0)
Main problems about geodesics (0)
From Random Polynomials to String Theory (2005) (0)
Real-analytic geodesics in the Mabuchi space of K\"ahler metrics and quantization (2022) (0)
Semi-classical Limit of Random Walks II 1 (1998) (0)
Ja n 20 08 Inverse resonance problem for Z 2-symmetric analytic obstacles in the plane ∗ (2008) (0)
Stability and integration over Bergman metrics (2014) (0)
Local and global analysis of nodal sets. (2018) (0)
Random Riesz energies on compact K (2011) (0)
Interfaces in Spectral Asymptotics and Nodal Sets (2020) (0)
Ju n 20 02 EQUILIBRIUM DISTRIBUTION OF ZEROS OF RANDOM POLYNOMIALS (2008) (0)
Random Complex Geometry , or How to count universes in string theory (2005) (0)
Geodesics and global harmonic analysis (2016) (0)
ERE EQUATION, II. LEGENDRE TRANSFORM (2010) (0)
SP ] 4 F eb 2 00 0 WAVE INVARIANTS FOR NON-DEGENERATE CLOSED GEODESICS (1998) (0)
2 0 Se p 20 04 Basic results in Vacuum Statistics (2008) (0)
$L^{\infty} $ norms of Husimi distributions of eigenfunctions (2020) (0)
LECTURES ON GEODESICS IN THE SPACE OF KAEHLER METRICS AND HELE-SHAW FLOWS: LECTURE 1 (2015) (0)
Geometry and large deviations for zeros of Gaussian random holomorphic polynomials on Riemann surfaces (2008) (0)
Off-Diagonal Decay of Toric Bergman Kernels (2016) (0)
Quantum Ergodic Sequences and Equilibrium Measures (2017) (0)
Zeros of real analytic ergodic Laplace eigenfunctions (2005) (0)
Scaling asymptotics of spectral Wigner functions (2022) (0)
Institute for Mathematical Physics Semi{classical Limit for Random Walks Semi-classical Limit for Random Walks 1 (1998) (0)
Statistics of supersymmetric vacua in string / M theory (2004) (0)
SP ] 9 A pr 2 00 3 QUANTUM ERGODICITY OF BOUNDARY VALUES OF EIGENFUNCTIONS (2002) (0)
Stochastic K\"ahler geometry: from random zeros to random metrics (2023) (0)
Feynman diagrams in inverse spectral theory (2004) (0)
Log-scale equidistribution of nodal sets in Grauert tubes (2018) (0)
Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces (2011) (0)
Thermodynamics of group representations (2004) (0)
What is a quantum Birkhoff normal form around a bouncing ball orbit ? (2004) (0)
Centrally symmetric analytic plane domains are spectrally determined in this class (2021) (0)
Lower bounds for Cauchy data on curves in a negatively curved surface (2021) (0)
Selberg trace formulae, PDO's and equidistribution theorems for closed geodesics and laplace eigenfunctions (1987) (0)

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