Charles L. Epstein is a Senior Research Scientist in the Center for Computational Mathematics at the Flatiron Institute. He is the Thomas A. Scott Professor of Mathematics Emeritus at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

, Philadelphia.CHARLES EPSTEIN NAMED THOMAS A. SCOTT PROFESSOR OF MATHEMATICS.

School of Arts and Sciences news release, February 2, 2010, accessed June 9, 2010.

Research areas

Charles Epstein is an analyst and

applied mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One ...

. His research interests include partial differential equations,

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

boundary value problem In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satis ...

mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development ...

population genetics Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as Adaptation (biology), adaptation, s ...

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

and

medical imaging Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to revea ...

, and

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

; he has also worked in hyperbolic geometry, univalent function theory, several complex variables,

microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes genera ...

and

index theory Index (: indexes or indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on the Halo Array in the ...

Education and career

He was an undergraduate in mathematics at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

and graduate student at the

Courant Institute The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

, where he received his

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1983 under the direction of

Peter Lax Peter David Lax (1 May 1926 – 16 May 2025) was a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax made important contributions to integrable systems, fluid dynamics an ...

. He was a postdoc with

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

before moving to the University of Pennsylvania, where he has been since. Epstein won a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in 1988. He is currently a Senior Research Scientist in the Center for Computational Mathematics at the Flatiron Institute, New York City, and Thomas A. Scott Professor of Mathematics Emeritus at the

, Philadelphia.

Awards and honors

In 2014, Charles Epstein became a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

"for contributions to analysis, geometry, and applied mathematics including medical imaging, as well as for service to the profession". He was a co-recipient of the

Stefan Bergman Prize The Stefan Bergman Prize is a mathematics award, funded by the estate of the widow of mathematician Stefan Bergman and supported by the American Mathematical Society. The award is granted for mathematical research in: "1) the theory of the kernel ...

in 2016.
merican Mathematical Society: Stefan Bergman Prize Laureates.

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. *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'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

'' 167 (1991), no. 1–2, 1–106. *C L Epstein, The hyperbolic Gauss map and quasiconformal reflections. ''

Journal für die Reine und Angewandte Mathematik ''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by A ...

'' 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 The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

'' (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 Spin_C Dirac operators. I. ''Annals of Mathematics'' (2) 166 (2007), no. 1, 183–214.

References

External links

*
Charles L. Epstein
webpage {{DEFAULTSORT:Epstein, Charles 21st-century American mathematicians 20th-century American mathematicians Living people University of Pennsylvania faculty Mathematicians at the University of Pennsylvania Fellows of the American Mathematical Society Courant Institute of Mathematical Sciences alumni Massachusetts Institute of Technology School of Science alumni Sloan Research Fellows Mathematicians from Pennsylvania Year of birth missing (living people)