H. Blaine Lawson

Distinguished Professor of Mathematics. Lawson is a leading differential geometer and founder, with R. Harvey, of calibrated geometries. These generalizations of Kähler geometry have fundamental applications in mathematics and physics which rival those of Kähler geometry itself. Lawson defined, and with collaborators, studied a bigraded homology theory for complex algebraic varieties, now called Lawson homology, which generalizes the group of algebraic cycles modulo algebraic equivalence in the same way that Bloch's higher Chow groups generalize the group of algebraic cycles modulo rational equivalence. Gromov and Lawson gave a theory of manifolds with positive scalar curvature that led to a nearly complete classification. For example, they proved that every compact simply-connected manifold of dimension greater than or equal to 5, which is not spin, carries a metric of positive scalar curvature. For spin manifolds they identified is a single spin-cobordism invariant which completed the story. Lawson, with Harvey, established a characterization of boundaries of complex analytic varieties, which represents a vast geometric generalization of the Bochner-Hartogs theory in several complex variables. Lawson has also contributed to foliations, minimal varieties, manifolds of non-positive section curvature, and nonlinear elliptic partial differential equations. He found the first codimension-one foliations of spheres of dimension > 3. He was the first to prove that every compact orientable surface can be minimally embedded in the 3-sphere. Lawson is a member of the National Academy of Sciences and the Brazilian Academy of Sciences.