Richard Schoen

Richard Schoen
Name	Richard Schoen
Birth date	1950
Birth place	United States
Fields	Mathematics; Differential geometry; Partial differential equation
Alma mater	University of California, Berkeley; University of California, Los Angeles
Doctoral advisor	Juha Heinonen
Known for	Yau–Tian–Donaldson conjecture; Positive mass theorem; Geometric analysis

Richard Schoen is an American mathematician noted for foundational work in Differential geometry, Geometric analysis, and the study of nonlinear Partial differential equation on manifolds. He made decisive contributions to the proof of the Positive mass theorem, the study of the Yamabe problem, and compactness results for conformal metrics, influencing research across Riemannian geometry, General relativity, and global analysis. Schoen has held professorships at major institutions and received multiple international prizes recognizing advances in Mathematics and its connections to Physics.

Early life and education

Schoen was born in the United States and completed undergraduate studies before pursuing graduate work at the University of California, Berkeley and the University of California, Los Angeles. During his doctoral training he engaged with research communities connected to Stanford University, Princeton University, and the Institute for Advanced Study. Early encounters with influences from scholars at Harvard University, Massachusetts Institute of Technology, and the American Mathematical Society shaped his trajectory toward problems linking Riemannian geometry and variational methods. Collaborations and mentorship networks included figures associated with Yale University, Columbia University, and the University of Chicago.

Mathematical career and positions

Schoen has served on the faculty of institutions such as University of California, Irvine, University of California, Berkeley, and University of California, Los Angeles before holding a long-term appointment at the University of California, San Diego. He has visited the Institute for Advanced Study, the Mathematical Sciences Research Institute, and research centers at Princeton University, Stanford University, and Oxford University. Schoen has lectured at conferences organized by the International Mathematical Union, the American Mathematical Society, and the Society for Industrial and Applied Mathematics. He has been involved with editorial boards for journals affiliated with the American Institute of Mathematics and universities such as Cambridge University Press and Springer Science+Business Media.

Major contributions and research

Schoen's work on the Yamabe problem with collaborators established existence and compactness results for constant scalar curvature metrics in conformal classes on compact Riemannian manifolds, connecting to techniques in Elliptic partial differential equation theory and the method of moving planes associated with works at Rutgers University and Duke University. In joint work on the Positive mass theorem and geometric inequalities he combined geometric measure theory traditions from Caltech and techniques influenced by research at the Courant Institute of Mathematical Sciences to address conjectures motivated by General relativity and results of researchers at Princeton University and Cambridge University. His joint studies with collaborators produced the Schoen–Yau results on minimal hypersurfaces, interacting with ideas developed at Columbia University and the Max Planck Institute for Mathematics.

Further contributions include analysis of scalar curvature rigidity phenomena linked to the Riemannian Penrose inequality and rigidity theorems that resonated with work at Imperial College London and ETH Zurich. Schoen explored compactness and blow-up analysis for conformal deformations, drawing upon techniques related to global regularity questions studied at Yale University and Brown University. He developed methods later applied to problems in conformal geometry, moduli of metrics, and the study of singularity formation, connecting to the research agendas of groups at International Centre for Theoretical Physics and the National Academy of Sciences.

Schoen's collaborations span many prominent mathematicians affiliated with institutions such as Columbia University, Stanford University, Harvard University, and the University of Cambridge, influencing subsequent developments in Geometric analysis and the interface between Topology and geometric PDE studied at Princeton University and Oxford University.

Awards and honors

Schoen's work has been recognized with major prizes and memberships, including awards administered by the National Academy of Sciences, the American Mathematical Society, and international honors from bodies associated with the International Mathematical Union. He has been elected to the National Academy of Sciences and received recognition from the American Academy of Arts and Sciences. He delivered plenary addresses at meetings of the International Congress of Mathematicians and received medals and prizes connected to institutions such as Princeton University, the Institute for Advanced Study, and national academies in Europe. His honors include fellowships and prizes from organizations linked to Simons Foundation, Clay Mathematics Institute, and major universities including Harvard University and Yale University.

Selected publications

- R. Schoen and S.-T. Yau, "Existence of a solution to the Yamabe problem", Annals of Mathematics; connects to literature from Princeton University and Columbia University. - R. Schoen, "Conformal deformation of a Riemannian metric to constant scalar curvature", Journal of Differential Geometry; situated alongside work from Harvard University and Stanford University. - R. Schoen and S.-T. Yau, "On the proof of the positive mass conjecture in general relativity", Communications in Mathematical Physics; relates to research themes at Caltech and Institute for Advanced Study. - R. Schoen, "Estimates for stable minimal surfaces", Annals of Mathematics; engages methods associated with Cambridge University and the Max Planck Institute for Mathematics. - R. Schoen and collaborators, "Compactness theorems for conformal metrics", Transactions of the American Mathematical Society; connected to seminars at University of Chicago and University of California, Berkeley.

Category:American mathematicians Category:Differential geometers