# Charles Epstein (mathematician)

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For the American geneticist, see [Charles Epstein (geneticist)](/source/Charles_Epstein_(geneticist)).

**Charles L. Epstein** is a Senior Research Scientist in the Center for Computational Mathematics at the Flatiron Institute. He was the [Thomas A. Scott Professor of Mathematics Emeritus](/source/Thomas_A._Scott_Professorship_of_Mathematics) at the [University of Pennsylvania](/source/University_of_Pennsylvania), Philadelphia.[2]

## Research areas

Charles Epstein is an [analyst](/source/Mathematical_analysis) and [applied mathematician](/source/Applied_mathematics). His research interests include partial differential equations, [mathematical physics](/source/Mathematical_physics), [boundary value problems](/source/Boundary_value_problem), [mathematical biology](/source/Mathematical_biology), [population genetics](/source/Population_genetics), [nuclear magnetic resonance](/source/Nuclear_magnetic_resonance) and [medical imaging](/source/Medical_imaging), and [numerical analysis](/source/Numerical_analysis); he has also worked in hyperbolic geometry, univalent function theory, several complex variables, [microlocal analysis](/source/Microlocal_analysis) and [index theory](/source/Index_theory).

## Education and career

He was an undergraduate in mathematics at the [Massachusetts Institute of Technology](/source/Massachusetts_Institute_of_Technology) and graduate student at the [Courant Institute](/source/Courant_Institute), [New York University](/source/New_York_University), where he received his [Ph.D.](/source/Ph.D.) in 1983 under the direction of [Peter Lax](/source/Peter_Lax).[3]

He was a postdoc with [William Thurston](/source/William_Thurston) before moving to the University of Pennsylvania, where he has been since. Epstein won a [Sloan Research Fellowship](/source/Sloan_Fellowship) in 1988.[2]

He is currently a Senior Research Scientist in the Center for Computational Mathematics at the Flatiron Institute, New York City, and was the [Thomas A. Scott Professor of Mathematics Emeritus](/source/Thomas_A._Scott_Professorship_of_Mathematics) at the [University of Pennsylvania](/source/University_of_Pennsylvania), Philadelphia.

## Awards and honors

In 2014, Charles Epstein became a Fellow of the [American Mathematical Society](/source/American_Mathematical_Society) "for contributions to analysis, geometry, and applied mathematics including medical imaging, as well as for service to the profession".[4] He was a co-recipient of the [Stefan Bergman Prize](/source/Stefan_Bergman_Prize) in 2016.[5]

## Books

- C L Epstein, Introduction to the mathematics of medical imaging. Second edition. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008. xxxiv+761 pp. ISBN 978-0-89871-642-9
- C L Epstein, The spectral theory of geometrically periodic hyperbolic 3-manifolds. Mem. Amer. Math. Soc. 58 (1985), No. 335, ix+161 pp.

## Selected publications

- C L Epstein, R B Melrose, G A Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains. *[Acta Mathematica](/source/Acta_Mathematica)* 167 (1991), no. 1–2, 1–106.
- C L Epstein, R Melrose, Contact degree and the index of Fourier integral operators. *Math. Res. Lett.* 5 (1998), no. 3, 363–381.
- C L Epstein, CR-structures on three-dimensional circle bundles. *Invent. Math.* 109 (1992), no. 2, 351–403.
- C L Epstein A relative index on the space of embeddable CR-structures. I. *[Annals of Mathematics](/source/Annals_of_Mathematics)* (2) 147 (1998), no. 1, 1–59.
- C L Epstein; G M Henkin, Stability of embeddings for pseudoconcave surfaces and their boundaries. *Acta Mathematica* 185 (2000), no. 2, 161–237.
- D Burns, C L Epstein, Characteristic numbers of bounded domains. *Acta Mathematica 164* (1990), no. 1–2, 29–71.
- D M Burns, Jr, C L Epstein, A global invariant for three-dimensional CR-manifolds. *Invent. Math.* 92 (1988), no. 2, 333–348.
- C L Epstein, B Kleiner, Spherical means in annular regions. *Comm. Pure Appl. Math.* 46 (1993), no. 3, 441–451.
- C L Epstein, Subelliptic Spin**C** Dirac operators. I. *Annals of Mathematics* (2) 166 (2007), no. 1, 183–214.

## References

1. [\[1\]](https://www.mathgenealogy.org/id.php?id=33693) Mathematics Genealogy Project

1. [CHARLES EPSTEIN NAMED THOMAS A. SCOTT PROFESSOR OF MATHEMATICS.](https://www.sas.upenn.edu/news/charles-epstein-named-thomas-scott-professor-mathematics) [University of Pennsylvania](/source/University_of_Pennsylvania) School of Arts and Sciences news release, February 2, 2010, accessed June 9, 2010.

1. [Charles L. Epstein, Curriculum Vitae](https://www.math.upenn.edu/~cle/cv.pdf), [University of Pennsylvania](/source/University_of_Pennsylvania) Department of Mathematics. Accessed June 9, 2016.

1. [List of Fellows of the American Mathematical Society](http://www.ams.org/profession/fellows-list)

1. [\[2\]](https://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=36) American Mathematical Society: Stefan Bergman Prize Laureates.

## External links

- [Charles L. Epstein](http://www.math.upenn.edu/~cle/) webpage

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