Celebrating The Schoenfest
Geometric Analysis:
Past, Current, And Future
Richard SCHOEN
Stanford University
About Professor Schoen
Professor Richard Schoen is a towering figure in mathematics who has fundamentally shaped modern geometric analysis. His seminal work, spanning decades, constitutes a series of foundational contributions.
Major Contributions
Foundational Work in Mathematical Physics
In a historic 1979 collaboration with Professor Shing-Tung Yau, Schoen established the Positive Mass Theorem. This was not merely an advance but a monumental clarification of the universe's basic structure, providing the rigorous mathematical proof that an isolated gravitational system must possess non-negative total energy. It remains a towering landmark, a definitive synthesis of geometric genius and profound physical insight.
Resolution of a Fundamental Problem
Schoen's 1984 conquest of the celebrated Yamabe Problem on compact manifolds was a masterstroke that forever altered the field. By definitively resolving this deep challenge concerning constant scalar curvature, he did more than close a chapter; he established nonlinear partial differential equations as a dominant force in geometric inquiry, single-handedly inspiring and enabling a generation of researchers.
Proof of a Landmark Conjecture
A testament to his sustained and unparalleled intellectual power, his 2007 proof of the Differentiable Sphere Theorem with Professor Simon Brendle delivered the final, elegant word on a central conjecture that had directed the course of global differential geometry for half a century. This was the crowning achievement of a decades-long intellectual quest, providing the complete and definitive characterization of the sphere.
These are not merely contributions; they are the pillars of the field. His collection of mathematics' most esteemed honors—including the Bôcher Memorial Prize, the Wolf Prize, and the WLA Prize—solidify his legacy as a true giant whose work will inspire generations to come.
Latest Recognition
2025 WLA Prize
The World Laureates Association (WLA) announced its laureates for 2025 in Shanghai in September, recognizing groundbreaking contributions in the fields of life and mathematical sciences. The 2025 WLA Prize in Computer Science or Mathematics was awarded to Richard Schoen, professor emeritus at the School of Humanities and Sciences at Stanford University, for his foundational work in geometric analysis and differential geometry, including seminal results on conformal partial differential equations, minimal surfaces, general relativity, harmonic maps and the Yamabe problem.
Prize Committee Statement
"Through revolutionary theorems, Schoen resolved problems once deemed intractable, created mathematical tools that redefined the framework of geometric analysis, and inspired generations of geometers with his pedagogical insights and pioneering approaches."