Charles Epstein

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Charles Epstein
Charles Epstein.png
BornPennsylvania, U.S.
Alma materMIT
Courant Institute
AwardsSloan Fellowship
Scientific career
Applied Mathematics
University of Pennsylvania
Doctoral advisorPeter Lax
Other academic advisorsWilliam Thurston

Charles L. Epstein is a Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, Philadelphia.[1]

Research interests[edit]

Epstein is an analyst and applied mathematician. His interests include microlocal analysis and index theory; boundary value problems; nuclear magnetic resonance and medical imaging; and mathematical biology.

Education and work[edit]

Charles Epstein was an undergraduate in mathematics at MIT and graduate student at the Courant Institute, NYU, where he received his PhD in 1983 under the direction of Peter Lax.[2]

He did a postdoc with William Thurston before moving to the University of Pennsylvania, where he has been since. Epstein won a Sloan Research Fellowship in 1988.[1]

He is currently Thomas A. Scott Professor of Mathematics and graduate chair of Applied Mathematics and Computational Science.

Awards and honors[edit]

In 2014, he became a Fellow of the American Mathematical Society "for contributions to analysis, geometry, and applied mathematics including medical imaging, as well as for service to the profession".[3]


  • 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.


  • C L Epstein, R B Melrose, G A Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains. Acta Mathematica 167 (1991), no. 1–2, 1–106.
  • C L Epstein, The hyperbolic Gauss map and quasiconformal reflections. Journal für die Reine und Angewandte Mathematik 372 (1986), 96–135.
  • 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, Embeddable CR-structures and deformations of pseudoconvex surfaces. I. Formal deformations. J. Algebraic Geom. 5 (1996), no. 2, 277–368.
  • C L Epstein, CR-structures on three-dimensional circle bundles. Invent. Math. 109 (1992), no. 2, 351–403.
  • D M Burns, C L Epstein, Embeddability for three-dimensional CR-manifolds. J. Amer. Math. Soc. 3 (1990), no. 4, 809–841.
  • C L Epstein A relative index on the space of embeddable CR-structures. I. Annals of Mathematics (2) 147 (1998), no. 1, 1–59.
  • C L Epstein, Asymptotics for closed geodesics in a homology class, the finite volume case. Duke Math. J. 55 (1987), no. 4, 717–757.
  • C L Epstein; G M Henkin, Stability of embeddings for pseudoconcave surfaces and their boundaries. Acta Mathematica 185 (2000), no. 2, 161–237.
  • C L Epstein, A relative index on the space of embeddable CR-structures. II. Annals of Mathematics (2) 147 (1998), no. 1, 61–91.
  • D Burns, C L Epstein, Characteristic numbers of bounded domains. Acta Mathematica 164 (1990), no. 1–2, 29–71.
  • C L Epstein, M Gage, The curve shortening flow. Wave motion: theory, modelling, and computation (Berkeley, Calif., 1986), 15–59, Math. Sci. Res. Inst. Publ., 7, Springer, New York, 1987.
  • 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, G M Henkin, Extension of CR-structures for 3-dimensional pseudoconcave manifolds. Multidimensional complex analysis and partial differential equations (São Carlos, 1995), 51–67, Contemp. Math., 205, Amer. Math. Soc., Providence, RI, 1997.
  • C L Epstein, B Kleiner, Spherical means in annular regions. Comm. Pure Appl. Math. 46 (1993), no. 3, 441–451.
  • C L Epstein, G M Henkin, Embeddings for 3-dimensional CR-manifolds. Complex analysis and geometry (Paris, 1997), 223–236, Progr. Math., 188, Birkhäuser, Basel, 2000.
  • C L Epstein, Subelliptic SpinC Dirac operators. I. Annals of Mathematics (2) 166 (2007), no. 1, 183–214.


  1. ^ a b CHARLES EPSTEIN NAMED THOMAS A. SCOTT PROFESSOR OF MATHEMATICS. University of Pennsylvania School of Arts and Sciences news release, February 2, 2010. Accessed June 9, 2010
  2. ^ Charles L. Epstein, Curriculum Vitae, University of Pennsylvania Department of Mathematics. Accessed June 9, 2016.
  3. ^ List of Fellows of the American Mathematical Society

External links[edit]