Wilfried Schmid
Encyclopedia
Wilfried Schmid is a German
-American
mathematician
who works in Hodge theory
, representation theory
, and automorphic form
s. He earned his Ph.D. at University of California, Berkeley
in 1967 under the direction of Phillip Griffiths
, and then taught at Berkeley and Columbia University
, becoming a Full Professor at Columbia at age 27. In 1978 he moved to Harvard University
, where he is currently the Dwight Parker Robinson Professor of Mathematics.
Schmid's early work concerns the construction of discrete series representation
s of semi-simple Lie group
s. Notable accomplishments here include a proof of Langlands' conjecture on the discrete series, along with a later proof (joint with Michael Atiyah
) constructing all such discrete series representations on spaces of harmonic spinors. Schmid along with his student Henryk Hecht proved Blattner's conjecture
in 1975. In the 1970s he described the singularities of the Griffith's period map by applying Lie-theoretic method
s to problems in algebraic geometry
.
Schmid has been very involved in K–12 mathematics education both nationally and internationally. His interest arose in 1999 after being disturbed by the experiences of his 2nd-grade daughter in her mathematics class. He was heavily involved in the drafting of the Massachusetts Mathematics Curriculum Framework in 2000. Later, he served on the National Mathematics Advisory Panel of the U.S. Department of Education.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
-American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who works in Hodge theory
Hodge theory
In mathematics, Hodge theory, named after W. V. D. Hodge, is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised...
, representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
, and automorphic form
Automorphic form
In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms...
s. He earned his Ph.D. at University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
in 1967 under the direction of Phillip Griffiths
Phillip Griffiths
Phillip Griffiths is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory.He received...
, and then taught at Berkeley and Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, becoming a Full Professor at Columbia at age 27. In 1978 he moved to Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, where he is currently the Dwight Parker Robinson Professor of Mathematics.
Schmid's early work concerns the construction of discrete series representation
Discrete series representation
In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation of the left regular representation of G on L²...
s of semi-simple Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. Notable accomplishments here include a proof of Langlands' conjecture on the discrete series, along with a later proof (joint with Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
) constructing all such discrete series representations on spaces of harmonic spinors. Schmid along with his student Henryk Hecht proved Blattner's conjecture
Blattner's conjecture
In mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group G in terms of their restricted representations to a maximal compact subgroup K . Harish-Chandra orally attributed the conjecture to Robert J Blattner,...
in 1975. In the 1970s he described the singularities of the Griffith's period map by applying Lie-theoretic method
Lie theory
Lie theory is an area of mathematics, developed initially by Sophus Lie.Early expressions of Lie theory are found in books composed by Lie with Friedrich Engel and Georg Scheffers from 1888 to 1896....
s to problems in algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
.
Schmid has been very involved in K–12 mathematics education both nationally and internationally. His interest arose in 1999 after being disturbed by the experiences of his 2nd-grade daughter in her mathematics class. He was heavily involved in the drafting of the Massachusetts Mathematics Curriculum Framework in 2000. Later, he served on the National Mathematics Advisory Panel of the U.S. Department of Education.