# Richard Schoen

Wolf Prize Laureate in Mathematics 2017

**Richard Schoen**

#### Affiliation at the time of the award:

**University of California, USA**

#### Award citation:

**“for their striking contributions to analysis and geometry”.**

#### Prize share:

**Richard Schoen**

**Charles Fefferman**

Richard Schoen (born in 1950) is one of the most recognized and outstanding mathematicians of our time. In the early years of his research career, he co-founded the then-new mathematical research field- geometric analysis. Since then, his vision, his insight, and his technical power led him to break countless barriers, open up numerous new research directions, and elevate our understanding of mathematical structure. Schoen is a leader in geometric analysis and its application to algebra, geometry, topology, differential equations, and mathematical physics.

Schoen’s fundamental contributions in several areas of geometric analysis fall into two main categories:

(a) the study of conformal geometry and scalar curvature, including applications to classical general relativity.

(b) the theory of minimal surfaces and harmonic maps, particularly the regularity theory of those.

The proof by Schoen (together with S.T. Yau) that energy is positive in General Relativity is a remarkable result, many people have tried to prove it without success, for half a century since Einstein invented his theory. What makes the problem so remarkable is that it is a fundamental statement, without which Einstein’s theory of Gravity would presumably not make much sense (at least from a quantum point of view), yet it is completely unclear why it is true. Neither Einstein nor any of his successors for half a century were able to clarify this. The theorem of Schoen and Yau is an unusual example in which a deep and rigorous mathematical theorem sheds light in an essential way on a central theory of modern physics.

**Richard Schoen is awarded the Wolf Prize for being a pioneer and a driving force in geometric analysis.**** His work on the regularity of harmonic maps and minimal surfaces had a lasting impact on the field. His solution of the Yamabe problem is based on the discovery of a deep connection to general relativity. Through his work on geometric analysis, Schoen has contributed greatly to our understanding of the interrelation between partial differential equations and differential geometry. Many of the techniques he developed continue to influence the advance of non-linear analysis.**