Richard Schoen
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Richard Melvin Schoen (b. October 23, 1950) is an American mathematician. Born in Fort Recovery, Ohio, he received his PhD from Stanford University where he is currently a Robert M. Bass Professor of Humanities and Sciences. He has two children, Lucy Schoen (born 4/25/1988) and Alan Schoen (born 2/29/1984), both current students at Stanford. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German ancestors.
Schoen is a world leader in 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, Schoen and fellow Stanford mathematician Simon Brendle proved the differentiable sphere theorem, an important result in the study of manifolds of positive sectional curvature.
