Biography:H. Blaine Lawson

Short description: American mathematician

H. Blaine Lawson, Jr.
H. Blaine Lawson in Berkeley, 1972
Born	(1942-01-04) January 4, 1942 Norristown, Pennsylvania
Citizenship	United States
Known for	Calibrated geometry Lawson's Klein bottle Hsiang–Lawson's conjecture
Awards	Leroy P. Steele Prize (1975)
Scientific career
Fields	Algebraic cycles Calibrated geometry Minimal surfaces
Institutions	Stony Brook University
Doctoral advisor	Robert Osserman
Doctoral students	Michael T. Anderson William Meeks, III Doris Fischer-Colbrie

Herbert Blaine Lawson, Jr. is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles. He is currently a Distinguished Professor of Mathematics at Stony Brook University. He received his PhD from Stanford University in 1969 for work carried out under the supervision of Robert Osserman.

Research

Minimal surfaces

Lawson found in 1970 a method to solve free boundary value problems for unstable Euclidean constant-mean-curvature surfaces by solving a corresponding Plateau problem for minimal surfaces in S³. He constructed compact minimal surfaces in the 3-sphere of arbitrary genus by applying Charles B. Morrey, Jr.'s solution of the Plateau problem in general manifolds. This work of Lawson contains a rich set of ideas, among them the conjugate surface construction for minimal and constant mean curvature surfaces.

Calibrated geometry

The theory of calibrations, whose roots are in the work of Marcel Berger, finds its genesis in a 1982 Acta Mathematica paper of Reese Harvey and Blaine Lawson. The theory of calibrations has grown to be important because of its many applications to gauge theory and mirror symmetry.

Algebraic cycles

In his 1989 Annals of Mathematics paper "Algebraic Cycles and Homotopy Theory", Lawson proved a theorem which is now called the Lawson suspension theorem. This theorem is the cornerstone of Lawson homology and morphic cohomology which are defined by taking the homotopy groups of algebraic cycle spaces of complex varieties.

Jeff Cheeger and H. Blaine Lawson (right) at a conference in 2007

These two theories are dual to each other for smooth varieties and have properties similar to those of Chow groups.

Awards and honors

He was a 1973 recipient of the American Mathematical Society's Leroy P. Steele Prize, and was elected to the National Academy of Sciences in 1995. He is a former recipient of both the Sloan Fellowship and the Guggenheim Fellowship, and has delivered two invited addresses at International Congresses of Mathematicians, one on geometry, and one on topology. He has served as Vice President of the American Mathematical Society, and is a foreign member of the Brazilian Academy of Sciences.

In 2012 he became a fellow of the American Mathematical Society. He was elected to the American Academy of Arts and Sciences in 2013.

Major publications

• Lawson, H. Blaine Jr. (1969). "Local rigidity theorems for minimal hypersurfaces". Annals of Mathematics. Second Series 89 (1): 187–197. doi:10.2307/1970816. 
• Lawson, H. Blaine Jr. (1970). "Complete minimal surfaces in S³". Annals of Mathematics. Second Series 92 (3): 335–374. doi:10.2307/1970625. 
• Hsiang, Wu-yi; Lawson, H. Blaine Jr. (1971). "Minimal submanifolds of low cohomogeneity". Journal of Differential Geometry 5 (1–2): 1–38. doi:10.4310/jdg/1214429775. 
• Lawson, H. Blaine Jr.; Yau, Shing Tung (1972). "Compact manifolds of nonpositive curvature". Journal of Differential Geometry 7 (1–2): 211–228. doi:10.4310/jdg/1214430828. 
• Lawson, H. Blaine Jr.; Simons, James (1973). "On stable currents and their application to global problems in real and complex geometry". Annals of Mathematics. Second Series 98 (3): 427–450. doi:10.2307/1970913. 
• Lawson, H. Blaine Jr. (1974). "Foliations". Bulletin of the American Mathematical Society 80 (3): 369–418. doi:10.1090/S0002-9904-1974-13432-4. 
• Harvey, F. Reese; Lawson, H. Blaine Jr. (1975). "On boundaries of complex analytic varieties. I". Annals of Mathematics. Second Series 102 (2): 223–290. doi:10.2307/1971032. 
• Gromov, Mikhael; Lawson, H. Blaine Jr. (1980). "Spin and scalar curvature in the presence of a fundamental group. I". Annals of Mathematics. Second Series 111 (2): 209–230. doi:10.2307/1971198. 
• Gromov, Mikhael; Lawson, H. Blaine Jr. (1980). "The classification of simply connected manifolds of positive scalar curvature". Annals of Mathematics. Second Series 111 (3): 423–434. doi:10.2307/1971103. 
• Bourguignon, Jean-Pierre; Lawson, H. Blaine Jr. (1981). "Stability and isolation phenomena for Yang–Mills fields". Communications in Mathematical Physics 79 (2): 189–230. doi:10.1007/BF01942061. Bibcode: 1981CMaPh..79..189B. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-79/issue-2/Stability-and-isolation-phenomena-for-Yang-Millsfields/cmp/1103908963.full. 
• Harvey, Reese; Lawson, H. Blaine Jr. (1982). "Calibrated geometries". Acta Mathematica 148: 47–157. doi:10.1007/BF02392726. 
• Gromov, Mikhael; Lawson, H. Blaine Jr. (1983). "Positive scalar curvature and the Dirac operator on complete Riemannian manifolds". Publications Mathématiques de l'Institut des Hautes Études Scientifiques 58: 83–196. doi:10.1007/BF02953774. http://www.numdam.org/item/PMIHES_1983__58__83_0/. 

Books

• Lawson, H. Blaine Jr. (1980). Lectures on minimal submanifolds. Vol. I. Mathematics Lecture Series. 9 (Second edition of 1977 original ed.). Wilmington, DE: Publish or Perish, Inc.. ISBN 0-914098-18-7. 
• Lawson, H. Blaine Jr. (1985). The theory of gauge fields in four dimensions. CBMS Regional Conference Series in Mathematics. 58. Providence, RI: American Mathematical Society. doi:10.1090/cbms/058. ISBN 0-8218-0708-0. 
• Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. 

See also

• Spin geometry

External links

• Homepage