The 1970 construction of minimal embeddings for every compact surface into the Euclidean 3-sphere established a foundational framework for understanding periodic surfaces of constant mean curvature. Since then, H. Blaine Lawson has produced a extensive body of research concerning algebraic cycles, Riemannian geometry, partial differential equations, and foliations, significantly shaping modern geometric topology and analysis.
Academic Foundation
Born in Norristown in 1942, Herbert Blaine Lawson Jr. pursued his early education at Brown University, graduating in 1964 with degrees in applied mathematics and Russian literature. He transitioned to Stanford University for his doctoral studies, completing his PhD in 1969 under the supervision of Robert Osserman. Following this, he joined the University of California, Berkeley, where he advanced to full professor before relocating to Stony Brook University in 1978. He continues his tenure there as a Distinguished Professor of Mathematics.
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Lawson’s work spans several complex variables and calibrated geometries. In collaboration with F. Reese Harvey, he identified submanifolds that bound complex analytic varieties and established significant classes of volume-minimizing submanifolds. This research, published in 1982, eventually influenced developments in M-theory within particle physics. Alongside S.-T. Yau, Lawson contributed to the study of manifolds with negative curvature, including the Splitting Theorem. Furthermore, his research with Mikhael Gromov on manifolds of positive scalar curvature utilized the Dirac operator to demonstrate that such metrics depend on the spin cobordism class of the manifold.
Algebraic Cycles and Topology
In his 1989 paper regarding algebraic cycles and homotopy theory, Lawson defined a new homology theory for algebraic geometry. Collaborating with Eric Friedlander, he developed morphic cohomology for algebraic varieties and successfully proved a Moving Lemma for cycle families. His extensive output also includes a book on Spin geometry co-authored with Marie-Louise Michelsohn, which serves as a technical resource for Atiyah-Singer index theorems, K-theory, and Clifford algebras.
International Contributions
Beyond his primary institutional affiliations, Lawson has served in extended visiting positions at international research facilities. These include the Institute for Advanced Study in Princeton, the Institut des Hautes Études Scientifiques near Paris, the Instituto de Matemática Pura e Aplicada in Rio de Janeiro, the Research Institute for Mathematical Sciences at Kyoto University, and the Tata Institute of Fundamental Research in Mumbai.
Fast facts
- Born: 1942, Norristown
- Citizenship: United States
- Education: Brown University (1964), Stanford University (1969)
- Current Position: Distinguished Professor, Stony Brook University
- Key Award: Leroy P. Steele Prize (1975)
- Professional Fellowships: American Mathematical Society (2013), American Academy of Arts and Sciences
Questions readers ask
What is Lawson’s primary field of research?
He specializes in areas including minimal surfaces, algebraic cycles, Riemannian geometry, and foliations.
Where has Lawson served as a professor?
He held faculty positions at the University of California, Berkeley, and Stony Brook University.
Achievements
- Leroy P. Steele Prize — 1975
- Held posts at University of California, Berkeley and Stony Brook University
- Fields: algebraic cycle
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