Nolan Russell Wallach (born August 3, 1940) is a mathematician known for work in the representation theory of
reductive algebraic group
In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group ''G'' over a perfect field is reductive if it has a representation with finite kernel which is a direc ...
s. He is the author of the 2-volume treatise ''Real Reductive Groups''.
Education and career
Wallach did his undergraduate studies at the
University of Maryland
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of M ...
, graduating in 1962.
[UCSD Mathematics Profile: Nolan Wallach](_blank)
, retrieved 2013-09-01. He earned his Ph.D. from
Washington University in St. Louis
Washington University in St. Louis (WashU or WUSTL) is a private research university with its main campus in St. Louis County, and Clayton, Missouri. Founded in 1853, the university is named after George Washington. Washington University is r ...
in 1966, under the supervision of Jun-Ichi Hano.
He became an instructor and then lecturer at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
. At
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...
he became in 1969 an assistant professor, in 1970 an associate professor, in 1972 a full professor, and in 1986 the Hermann Weyl Professor of Mathematics. In 1989 he became a professor at the
University of California, San Diego
The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...
, where he is now a professor emeritus. From 1997 to 2003 he was an associate editor of the
Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
and from 1996 to 1998 an associate editor of the
Bulletin of the American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society.
Scope
It publishes surveys on contemporary research topics, written at a level accessible to non-experts. I ...
.
Wallach was a Sloan Fellow from 1972 to 1974. In 1978 he was an Invited Speaker with talk ''The spectrum of compact quotients of semisimple Lie groups'' at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in Helsinki. He was elected in 2004 a Fellow of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
and in 2012 a Fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
His doctoral students include AMS Fellow
Alvany Rocha.
He has supervised more than 18 Ph.D. theses.
Besides representation theory, Wallach has also published more than 150 papers in the fields of algebraic geometry, combinatorics, differential equations, harmonic analysis, number theory, quantum information theory, Riemannian geometry, and ring theory.
Selected publications
Articles
*with Michel Cahen: Lorentzian symmetric spaces, Bull. Amer. Math. Soc., vol. 76, no. 3, 1970, pp. 585–591.
*with
M. do Carmo: Minimal immersions of spheres into spheres, Annals of Mathematics, vol. 93, 1971, pp. 43–62.
*Compact homogeneous Riemannian manifolds with strictly positive curvature, Annals of Mathematics, vol. 96, 1972, pp. 277–295.
*with S. Aloff: An infinite number of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc., vol. 81, 1975, pp. 93–97
*with D. DeGeorge: Limit formulas for multiplicities in L
2(Γ\G), Annals of Mathematics, vol. 107, 1978, pp. 133–150.
*with Roe Goodman: Classical and quantum mechanical systems of Toda lattice type, 3 Parts, Comm. Math. Phys., Part I, vol. 83, 1982, pp. 355–386, ; Part II, vol. 94, 1984, pp. 177–217, ; Part III, vol. 105, 1986, pp. 473–509,
*with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57–75
*with A. Rocha-Caridi: Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas, Transactions of the American Mathematical Society, vol. 277, 1983, pp. 133–162
*with T. Enright,
R. Howe: A classification of unitary highest weight modules, in: Representation theory of reductive groups (Park City, Utah 1982), Progress in Mathematics 40, Birkhäuser 1983, pp. 97–143
*with A. Rocha-Caridi
Characters of irreducible representations of the Virasoro-Algebra Mathematische Zeitschrift, vol. 185, 1984, pp. 1–21
* Invariant differential operators on a reductive Lie algebra and Weyl group representations, J. Amer. Math. Soc., vol. 6, no. 4, 1993, pp. 779–816.
*Quantum computing and entanglement for mathematicians, in: Representation theory and complex analysis, pp. 345–376, Lecture Notes in Math. No. 1931, Springer 2008
*with G. Gour: Classification of multipartite entanglement of all finite dimensionality, Phys. Rev. Lett., vol. 111, 2013, 060502
Books
*Harmonic analysis on homogeneous spaces, New York: Marcel Dekker 1973
*Symplectic geometry and Fourier analysis, Brookline: Math. Science Press 1977
*Real Reductive Groups, 2 vols., Academic Press 1988, 1992
*with Roe Goodman: Representations and invariants of the classical groups, Cambridge University Press 1998; 1st pbk edition, 1999
reprint with corrections 2003
*with
Armand Borel
Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in alg ...
: Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Mathematical Studies 94, 1980
2nd edition American Mathematical Society 2013
*with Roe Goodman
Symmetry, representations, and invariants Graduate Texts in Mathematics, Springer 2009
Geometric Invariant Theory: Over the Real and Complex Numbers Universitext, Springer 2017
References
External links
Personal website
'
{{DEFAULTSORT:Wallach, Nolan
20th-century American mathematicians
21st-century American mathematicians
University of Maryland, College Park alumni
Washington University in St. Louis alumni
Washington University in St. Louis mathematicians
Rutgers University faculty
University of California, San Diego faculty
Fellows of the American Academy of Arts and Sciences
Fellows of the American Mathematical Society
1940 births
Living people
University of California, Berkeley College of Letters and Science faculty