Richard Schoen

Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry.

Richard Schoen
Richard Schoen in 1976
(photo by George Bergman)
Born (1950-10-23) October 23, 1950
Fort Recovery, Ohio[1]
NationalityAmerican
Alma materStanford University
Known for
Spouse(s)Doris Fischer-Colbrie
Awards
Scientific career
FieldsMathematics
InstitutionsStanford University
University of California, Berkeley
University of California, Irvine
Doctoral advisor
Doctoral students

Born in Celina, Ohio, and a 1968 graduate of Fort Recovery High School, he received his B.S. from the University of Dayton in mathematics. He then received his PhD in 1977 from Stanford University and is currently an Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German ancestors.

Schoen is a 1983 MacArthur Fellow.

Contributions

Schoen has investigated the use of analytic techniques in global differential geometry. In 1979, together with his former doctoral supervisor, Shing-Tung Yau, he proved the fundamental positive energy theorem in general relativity. In 1983, he was awarded a MacArthur Fellowship, and in 1984, he obtained a complete solution to the Yamabe problem on compact manifolds. This work combined new techniques with ideas developed in earlier work with Yau, and partial results by Thierry Aubin and Neil Trudinger. The resulting theorem asserts that any Riemannian metric on a closed manifold may be conformally rescaled (that is, multiplied by a suitable positive function) so as to produce a metric of constant scalar curvature. In 2007, Simon Brendle and Richard Schoen proved the differentiable sphere theorem, a fundamental result in the study of manifolds of positive sectional curvature. He has also made fundamental contributions to the regularity theory of minimal surfaces and harmonic maps.

His students include Hubert Bray, José F. Escobar, Ailana Fraser, Chikako Mese, William Minicozzi, and André Neves.[4]

Awards and honors

For his work on the Yamabe problem, Schoen was awarded the Bôcher Memorial Prize in 1989. He joined the American Academy of Arts and Sciences in 1988 and the National Academy of Sciences in 1991, and won a Guggenheim Fellowship in 1996. In 2012 he became a fellow of the American Mathematical Society.[5] In 2015, he was elected Vice President of the American Mathematical Society.[6] He received the Wolf Prize in Mathematics for 2017, shared with Charles Fefferman.[7] In the same year, he was awarded the Lobachevsky Medal and Prize by Kazan Federal University.[8]

Selected publications
  • Schoen, Richard M.; Simon, Leon; Yau, Shing-Tung (1975), "Curvature estimates for minimal hypersurfaces", Acta Mathematica, 134 (3–4): 275–288, doi:10.1007/bf02392104, MR 0423263
  • Schoen, Richard M.; Yau, Shing-Tung (1979), "On the proof of the positive mass conjecture in general relativity", Communications in Mathematical Physics, 65 (1): 45–76, Bibcode:1979CMaPh..65...45S, doi:10.1007/bf01940959, MR 0526976
  • Fischer-Colbrie, Doris; Schoen, Richard M. (1980), "The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature", Communications on Pure and Applied Mathematics, 33 (2): 199–211, doi:10.1002/cpa.3160330206, MR 0562550
  • Schoen, Richard M.; Yau, Shing-Tung (1981), "Proof of the positive mass theorem. II", Communications in Mathematical Physics, 79 (2): 231–260, Bibcode:1981CMaPh..79..231S, doi:10.1007/bf01942062, MR 0612249
  • Schoen, Richard M.; Uhlenbeck, Karen (1982), "A regularity theory for harmonic maps", Journal of Differential Geometry, 17 (2): 307–335, MR 0664498
  • Schoen, Richard M. (1984), "Conformal deformation of a Riemannian metric to constant scalar curvature", Journal of Differential Geometry, 20 (2): 479–495, MR 0788292
  • Gromov, Mikhael; Schoen, Richard M. (1992), "Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one", Institut des Hautes Études Scientifiques. Publications Mathématiques, 76: 165–246, doi:10.1007/bf02699433, MR 1215595
  • Schoen, Richard M.; Wolfson, Jon (2001), "Minimizing area among Lagrangian surfaces: the mapping problem", Journal of Differential Geometry, 58 (1): 1–86, arXiv:math/0008244, MR 1895348
  • Brendle, Simon; Schoen, Richard M. (2009), "Manifolds with 1/4-pinched curvature are space forms", Journal of the AMS, 22 (1): 287–307, arXiv:0705.0766, Bibcode:2009JAMS...22..287B, doi:10.1090/s0894-0347-08-00613-9, MR 2449060
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References
  1. "Richard Melvin Schoen". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 6 January 2017.
  2. "Richard Schoen Announced as the Winner of the 2017 Lobachevsky Medal and Prize".
  3. http://www.rolfschockprizes.se/download/18.39ee338a159fb6d5d78e05/1489565086195/pop_matematik_en_170314_FINAL.pdf
  4. "Richard Schoen - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2019-03-12.
  5. List of Fellows of the American Mathematical Society, retrieved 2013-07-14.
  6. "American Mathematical Society". Retrieved 25 May 2016.
  7. The Wolf Foundation – "Richard Schoen Winner of Wolf Prize in Mathematics - 2017"
  8. Lobachevsky Medal and Prize Awarded to Richard Schoen
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