H. Blaine Lawson

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.[3]

H. Blaine Lawson, Jr.
H. Blaine Lawson in Berkeley, 1972
Born (1942-01-04) January 4, 1942[1]
Norristown, Pennsylvania[2]
CitizenshipUnited States
Known forCalibrated geometry
Lawson's Klein bottle
Hsiang–Lawson's conjecture
AwardsLeroy P. Steele Prize (1975)
Scientific career
FieldsAlgebraic cycles
Calibrated geometry
Minimal surfaces
InstitutionsStony Brook University
Doctoral advisorRobert Osserman
Doctoral studentsMichael T. Anderson
William Meeks, III
Doris Fischer-Colbrie

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.[4] He was elected to the American Academy of Arts and Sciences in 2013.[5]

Major publications

Books

  • Lawson, H. Blaine, Jr. (1980). Lectures on minimal submanifolds. Vol. I. Mathematics Lecture Series. Vol. 9 (Second edition of 1977 original ed.). Wilmington, DE: Publish or Perish, Inc. ISBN 0-914098-18-7. MR 0576752. Zbl 0434.53006.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Lawson, H. Blaine, Jr. (1985). The theory of gauge fields in four dimensions. CBMS Regional Conference Series in Mathematics. Vol. 58. Providence, RI: American Mathematical Society. doi:10.1090/cbms/058. ISBN 0-8218-0708-0. MR 0799712. Zbl 0597.53001.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Lawson, H. Blaine, Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.{{cite book}}: CS1 maint: multiple names: authors list (link)

See also

References
  1. Date information sourced from Library of Congress Authorities data, via corresponding WorldCat Identities linked authority file (LAF).
  2. "Lawson, Herbert Blaine". American Men and Women of Science. Vol. 4 (21st ed.). Bowker. 2009. ISBN 9780787665272.
  3. H. Blaine Lawson at the Mathematics Genealogy Project
  4. List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
  5. Newly elected members Archived 2013-05-01 at the Wayback Machine, American Academy of Arts and Sciences, April 2013, retrieved 2013-04-24.
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