H. Blaine Lawson
Encyclopedia
Blaine Lawson is a mathematician best known for his work in minimal surface
s, calibrated geometry
, and algebraic cycles. His current position is
Distinguished Professor at the State University of New York at Stony Brook
. He received his PhD from Stanford University
in 1969 for worked carried out under the supervision of Robert Osserman
. He was a 1973 recipient of the American Mathematical Society's Leroy P. Steele Prize, and was elected to the US National Academy of Sciences
in 1995. He is a former recipient of both Sloan and Guggenheim Foundation fellowships, 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.
surface
s 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 Morrey
's solution of the Plateau problem in general manifold
s. This work of Lawson contains a rich set of ideas among them the conjugate surface construction for minimal and constant mean curvature surfaces.
, 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
.
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 group
s of algebraic cycle spaces of complex varieties. These two theories are dual to each other for smooth varieties and have properties similar to those of Chow groups.
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....
s, calibrated geometry
Calibrated geometry
In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold of dimension n equipped with a differential p-form φ which is a calibration in the sense that...
, and algebraic cycles. His current position is
Distinguished Professor at the State University of New York at Stony Brook
State University of New York at Stony Brook
The State University of New York at Stony Brook, also known as Stony Brook University, is a public research university located in Stony Brook, New York, on the North Shore of Long Island, about east of Manhattan....
. He received his PhD from Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
in 1969 for worked carried out under the supervision of Robert Osserman
Robert Osserman
Robert Ossermanis an American mathematician.Raised in Bronx, he went to Bronx High School of Science and New York University.He earned a Ph.D...
. He was a 1973 recipient of the American Mathematical Society's Leroy P. Steele Prize, and was elected to the US National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1995. He is a former recipient of both Sloan and Guggenheim Foundation fellowships, 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.
Minimal surfaces
Lawson found in 1970 a method to solve free boundary value problems for unstable Euclidean constant-mean-curvatureMean curvature
In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space....
surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
s by solving a corresponding Plateau problem for minimal surfaces in S3. He constructed compact minimal surfaces in the 3-sphere
3-sphere
In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space...
of arbitrary genus by applying Morrey
Charles B. Morrey, Jr.
Charles Bradfield Morrey Jr. was an American mathematician who made fundamental contributions to the calculus of variations and the theory of partial differential equations.- Life :Charles Bradfield Morrey Jr...
's solution of the Plateau problem in general manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s. 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 BergerMarcel Berger
Marcel Berger is a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques , France...
, 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
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
and mirror symmetry
Mirror symmetry
In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden...
.
Algebraic cycles
In his 1989 Annals of MathematicsAnnals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
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 group
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space...
s of algebraic cycle spaces of complex varieties. These two theories are dual to each other for smooth varieties and have properties similar to those of Chow groups.