University of Pennsylvania
|Doctoral advisor||Peter Lax|
|Other academic advisors||William Thurston|
|Notable awards||K. O. Friedrichs Prize|
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 and graduate chair of Applied Mathematics and Computational Science.
Epstein is married and has two children.
Charles Epstein received the K. O. Friedrichs Prize of the Courant Institute.
- 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 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 SpinC Dirac operators. I. Annals of Mathematics (2) 166 (2007), no. 1, 183–214.