Richard Schoen

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Richard Melvin Schoen (pronounced Schejn; born October 23, 1950 in Celina , Ohio ) is an American mathematician who deals with global analysis and differential geometry.

Richard Schoen

Schoen received his PhD from Stanford University in 1977 with Leon Simon and Shing-Tung Yau (Existence and Regularity Theorems for some Geometric Variational Problems). He then was an Assistant Professor at the Courant Institute of Mathematical Sciences of New York University . In 1979/80 he was at the Institute for Advanced Study . In the 1980s he was a professor at the University of California, Berkeley , then at Stanford University, where he was Robert M. Bass Professor of Humanities and Sciences . He has been a Distinguished Professor at the University of California, Irvine since 2014 .

1979 Schoen and Yau proved the positivity of energy in general relativity . Edward Witten gave an alternative proof in 1981 and extensions have been proven by various mathematicians and physicists (such as Stephen Hawking , Gary Horowitz , Malcolm Perry). In 1984 he completely solved the Yamabe problem for compact manifolds, building on work with Yau and by Thierry Aubin and Neil Trudinger . It says that any Riemann metric of a smooth, compact manifold with three or more dimensions conforms to a metric of constant scalar curvature. In 2007 Simon Brendle and Richard Schoen proved the Differentiable Sphere Theorem . It states that a complete, simply connected n-dimensional Riemannian manifold whose sectional curvature (Sectional Curvature) K larger than 1 / 4 and less than or equal to 1 (K = 1 corresponds to the sphere), diffeomorphic to the n-sphere.

In 1983 he received a MacArthur Fellowship . In 1988 he was elected to the American Academy of Arts and Sciences , and in 1991 to the National Academy of Sciences . In 1989 he received the Bôcher Memorial Prize . In 2017 he was awarded the Wolf Prize in Mathematics and the Rolf Schock Prize in Mathematics. He was also awarded the Heinz Hopf Prize and the Lobatschewski Medal for 2017 . He was invited speaker at the ICM 1986 in Berkeley ( New Developments in the theory of geometric partial differential equations ) and 1983 in Warsaw ( Minimal surfaces and positive scalar curvature ). In 2010 he gave a plenary lecture at the International Congress of Mathematicians in Hyderabad ( Riemannian manifolds of positive curvature ). He is a fellow of the American Mathematical Society . In 1979 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

Web links

Individual evidence

  1. ↑ Member Book Institute Advanced Study
  2. ^ Schoen, Yau On the positive mass conjecture in general relativity , Commun. Math. Phys., Vol. 65, 1979, p. 45, Proof of the positive mass theorem. II , Commun. Math. Phys., Vol. 79, 1981, p. 231, expanded to include the Bondi mass by Schoen, Yau Proof that the Bondi mass is positive , Physical Review Letters, Vol. 48, 1982, p. 369
  3. ^ Conformal deformation of a Riemannian metric to constant scalar curvature, Journal of Differential Geometry, Vol. 20, 1984, pp. 479-495
  4. ↑ Brendle, Schoen Manifolds with 1/4 pinched curvature are space forms , Journal of the AMS, Vol. 22, 2009, p. 287, Classification of manifolds with 1/4 pinched curvature , Acta Mathematica, Vol. 200, 2008, p 1., Brendle, Schoen Curvature, sphere theorems and the Ricci flow , Bulletin AMS, Volume 48, 2011, pp. 1-32
  5. ↑ In the Sphere Theorem only homeomorphism is asserted, proven by Marcel Berger and Wilhelm Klingenberg in 1960
  6. ↑ Rolf Schock Prize 2017
personal data
SURNAME Fine, Richard
ALTERNATIVE NAMES Schoen, Richard Melvin (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH October 23, 1950
PLACE OF BIRTH Celina , Ohio