Richard Schoen

Richard Schoen
Richard Schoen (photo by George Bergman)
Born	(1950-10-23) October 23, 1950 (age 66) Fort Recovery, Ohio
Nationality	American
Fields	Mathematics
Institutions	Stanford University University of California, Berkeley University of California, Irvine
Alma mater	Stanford University
Doctoral advisor	Leon Simon Shing-Tung Yau
Doctoral students	Hubert Bray José F. Escobar Ailana Fraser Robert Kusner Mario Micallef William Minicozzi André Neves
Known for	Differentiable sphere theorem Schoen–Yau conjecture Solution of positive mass conjecture
Notable awards	Bôcher Memorial Prize (1989) Wolf Prize (2017)

Richard Melvin Schoen (born October 23, 1950) is an American mathematician. 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 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.