Charles L. Epstein is a Thomas A. Scott Professor of Mathematics at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, 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 interests

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 interests include

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 (or its plural form 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 a Halo megastru ...

;

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed 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 rev ...

; and

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

Education and work

Epstein was an undergraduate in mathematics at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

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), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

, where he received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

in 1983 under the direction of

Peter Lax Peter David Lax (born Lax Péter Dávid; 1 May 1926) is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax has made important contributions to integrable systems, fluid dyn ...

. He did 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. Thurston ...

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 Thomas A. Scott Professor of Mathematics and serves as graduate chair of Applied Mathematics and Computational Science from 2008 to June 2019.

Awards and honors

In 2014, he 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".List of Fellows of the American Mathematical Society
/ref>

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 Augus ...

'' 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 the ...

'' (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)