Charles Epstein is Professor of Mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 at the University of Pennsylvania

University of Pennsylvania

The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...

, Philadelphia.

Research interests

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

Education and work

Charles Epstein was an undergraduate in mathematics at MIT and graduate student at the Courant Institute, NYU, where he received his PhD. He did a postdoc with William Thurston before moving to the University of Pennsylvania, where he has been since. He is currently Thomas A. Scott Professor of Mathematics

Thomas A. Scott Professorship of Mathematics

The Thomas A. Scott Professorship of Mathematics is an academic grant made to the University of Pennsylvania. It was established in 1881 by the railroad executive and financier: Thomas Alexander Scott.-Recipients:*Ezra Otis Kendall, 1881 – 1899...

 and graduate chair of Applied Mathematics and Computational Science.

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.

Publications

• C L Epstein, R B Melrose, G A Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains. Acta Mathematica
  Acta Mathematica
  Acta Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
  
   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
  Annals of Mathematics
  The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
  
  (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 Math. (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 Spin_C Dirac operators. I. Annals of Mathematics (2) 166 (2007), no. 1, 183–214.

External links

• Charles L. Epstein webpage