Steven Zelditch
Steven Morris Zelditch , also Steve Zelditch, (born September 13, 1953 ) is an American mathematician who deals with global analysis with application to quantum chaos , with complex geometry and mathematical physics.
Zelditch studied at Harvard University with a bachelor's degree in mathematics in 1975 and received his doctorate in 1981 from the University of California, Berkeley with Alan Weinstein (Reconstruction of singularities of solutions for Schrödinger's equations). As a post-graduate student , he was Ritt Assistant Professor at Columbia University and Berkeley. In 1985 he became Assistant Professor, 1989 Associate Professor and 1992 Professor of Mathematics at Johns Hopkins University . From 2010 he was a professor at Northwestern University . He is Wayne and Elizabeth Jones Professor there.
In 1987/88 he was at MIT and in 1988 visiting professor at MSRI .
He deals with the spectral and scattering theory of the Laplace operator on Riemann manifolds and especially the asymptotics and distribution of its eigenfunctions (e.g. quantum ergodicity in billiard geometries) and the inverse spectral problem ( Can you hear the shape of a drum? According to Mark Kac ). Other research topics are Bergman kernels, Kähler metrics, Gaussian random waves and random metrics.
In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing ( Asymptotics of polynomials and eigenfunctions ). He is a fellow of the American Mathematical Society .
In 2013 he and Xiaojun Huang received the Stefan Bergman Prize, Zelditch especially for work on the Bergman core.
He is co-editor of Communications in Mathematical Physics, Analysis & PDE, and the Journal of Geometric Analysis.
Fonts
- Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Mathematical Journal, Volume 55, 1987, pp. 919-941
- with Maciej Zworski : Ergodicity of eigenfunctions for ergodic billiards, Comm. Math. Phys., Vol. 175, 1996, 673-682
- with B. Shiffman: Distribution of zeros of random and quantum chaotic sections of positive line bundles, Communications in mathematical physics, Volume 200, 1999, pp. 661-683
- with Pavel Bleher , B. Shiffman: Universality and scaling of correlations between zeros on complex manifolds, Inventiones mathematicae, Volume 142, 2000, pp. 351–395
- Reconstruction of singularities for solutions of Schrödinger's equation, Communications in Mathematical Physics, Volume 90, 1983, pp. 1-26
- Selberg trace formulas and equidistribution theorems for closed geodesics and Laplace eigenfunctions: finite area surfaces, American Mathematical Society 1992
- IAS / Park City Lectures on Eigenfunctions 2013
- Eigenfunctions and nodal sets, Surveys in Differential Geometry, Volume 18, 2013, 237-308
- with Frank Ferrari, Semyon Klevtsov: Random Geometry, Quantum Gravity and the Kähler Potential, Phys. Lett. B. 705, 2011
- Recent developments in mathematical quantum chaos, Current Developments in Mathematics 2009
- Local and Global Analysis of Eigenfunctions, Handbook of Geometric Analysis, Volume 1, 2008
- Complex zeros of real ergodic eigenfunctions, Invent. Math. 167 (2007), 419--443, Arxiv
- Survey of the inverse spectral problem, Surveys in Diff. Geom., 2004
- From random polynomials to symplectic geometry, Proc. Boarding school Congress Math. Phys. 2000
- Quantum Ergodicity of C * Dynamical Systems, Comm. Math. Phys., 177,1996, 507-528
- Mathematics of quantum chaos 2019: intersections of a curve with a nodal line on a hyperbolic surface, Notices of the AMS, October 2019
Web links
Individual evidence
- ↑ Steven Zelditch in the Mathematics Genealogy Project (English)
- ↑ Notices AMS, April 2014, pdf
personal data | |
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SURNAME | Zelditch, Steven |
ALTERNATIVE NAMES | Zelditch, Steve |
BRIEF DESCRIPTION | American mathematician |
DATE OF BIRTH | September 13, 1953 |