Harold Widom

Harold Widom (born 1932) is an American mathematician, born in New York City and well known for his contributions to
operator theory and random matrices.

Education and research

Harold Widom studied at Stuyvesant High School (graduated 1949) which herepresented as a member of their math team, along with his brother Benjamin Widom (1944, 1948). [ [http://www.widom.com Widom family webpage] ] Next, he obtained a B.Sc.in mathematics from City College of New York (1951), during which he was one of the winners of the
William Lowell Putnam Mathematical Competition (1951). At the University of Chicago he obtained an M.S. (1952)and Ph.D., the latter on a thesis "Embedding of AW*-algebras" advised by Irving Kaplansky (1955). [ [http://genealogy.math.ndsu.nodak.edu/id.php?id=845 entry] at Mathematics Genealogy Project.] He taught mathematics at Cornell University (1955-68) where he started his work on
Toeplitz and Wiener-Hopf operators, partly inspired by Mark Kac.He was appointed in the Department of Mathematics at the University of California, Santa Cruz in 1968; he became professor emeritus in 1994.

His research areas [ [http://math.ucsc.edu/~widom/widom.html homepage] at UCSC.] were
integral equations and
operator theory, in particular the determination of the spectra of a semi-infinite Toeplitz matrix and Wiener-Hopf operators, and the asymptotic behavior of the spectra of various classes of operators. The latter was looked at from the point of view of pseudodifferential operators (which generalize both integral and partial differential operators) on manifolds.

More recently, his mathematical contributions with his long term collaborator Craig Tracy have been recognized through the award of several prizes for their joint work on "Tracy-Widom distribution functions" for random matrices. They used integral operators to obtain explicit representations, in terms of Painlevé transcendents, of the limiting distributions of the largest and smallest eigenvalues in many models of random matrices (see Fredholm determinants). These same distributions have since been shown to arise in numerous other physical models, in random growth models, and in asymptotic combinatorics.

He has edited two books, authored more than 120 journal articles, and is an associate editor of Asymptotic Analysis,Journal of Integral Equations and Applications andMathematical Physics, Analysis and Geometry.He is an honorary editor of Integral Equations andOperator Theory.

Awards

*Norbert Wiener Prize in Applied Mathematics 2006, shared with Craig Tracy [http://www.ams.org/notices/200704/comm-wiener-web.pdf 2007 Wiener Prize] ]
*American Academy of Arts and Sciences electee, 2006
*George Polya Prize 2002, shared with Craig Tracy, for their work on random matrices
*Guggenheim Fellow 1967 and 1972
*Sloan Fellowship 1964–65
*National Science Foundation Postdoctoral Fellowship, 1959–60

Notes

Bibliography

*citation|title=Toeplitz Operators and Related Topics: The Harold Widom Anniversary Volume : Workshop on Toeplitz and Wiener–Hopf Operators, Santa Cruz, California, September 20–22, 1992|first=Estelle L.|last= Basor|first2=Israel|last2= Gohberg|authorlink2=Israel Gohberg|publisher=Birkhäuser|year=1994
id=ISBN 3764350687|series=Oper. Theory Adv. Appl.|volume= 71. (The proceedings of this 60th birthday conference contain a short biography by Estelle L. Basor and Edward M. Landesman.)