Lawrence Clinton Washington (born 1951,
Vermont) is an American mathematician at the
University of Maryland who specializes in
number theory.
Biography
Washington studied at
Johns Hopkins University, where in 1971 he received his B.A. and master's degree. In 1974 he earned his PhD at
Princeton University under
Kenkichi Iwasawa with thesis ''Class numbers and
extensions''. He then became an assistant professor at
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
and from 1977 at the
University of Maryland, where he became in 1981 an associate professor and in 1986 a professor. He held visiting positions at several institutions, including
IHES (1980/81),
Max-Planck-Institut für Mathematik
The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck
and forms part of the Max Planck So ...
(1984), the
Institute for Advanced Study (1996), and
MSRI (1986/87), as well as at the
University of Perugia,
Nankai University
Nankai University (NKU or Nankai; ) is a national public research university located in Tianjin, China. It is a prestigious Chinese state Class A Double First Class University approved by the central government of China, and a member of the fo ...
and the
State University of Campinas. In 1979–1981 he was a
Sloan Fellow.
Recognition
He was named to the 2023 class of Fellows of the
American Mathematical Society, "for contributions to number theory, especially cyclotomic fields, and for mentoring at all levels".
Research
Washington wrote a standard work on
cyclotomic fields. He also worked on
p-adic L-functions. He wrote a treatise with Allan Adler on their discovery of a connection between higher-dimensional analogues of
magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
s and p-adic L-functions. Washington has done important work on
Iwasawa theory,
Cohen-
Lenstra heuristics, and
elliptic curves and their applications to
cryptography.
In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of
Kenkichi Iwasawa, that the
-invariant vanishes for cyclotomic Z
''p''-extensions of
abelian number field
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.
Hilbert is credit ...
s (
Theorem of Ferrero-Washington).
[Ferrero, Washington ''The Iwasawa invariant μp vanishes for abelian number fields'', Annals of Mathematics, vol. 109, 1979, pp. 377–395. Another proof was provided by W. Sinnott, Inventiones Mathematicae, vol. 75, 1984, 273.]
More recently, Washington has published on arithmetic dynamics, sums of powers of primes, and Iwasawa invariants of non-cyclotomic Z
''p'' extensions
Selected works
''Introduction to Cyclotomic Fields'' Graduate Texts in Mathematics, Springer, 1982, 2nd edn. 1996
* ''Galois Cohomology'' in Cornell, Silverman, Stevens (eds.): ''Modular forms and Fermat's Last Theorem'', Springer, 1997
''Elliptic Curves: Number theory and cryptography'' CRC Press, 2003, 2nd edn. 2008
* with James Kraft: ''An Introduction to Number Theory with Cryptography'', CRC Press, 2003, 2nd edn.
* with Wade Trappe: ''Introduction to Cryptography and Coding Theory'', Prentice-Hall, 2002, 2nd edn. 2005
Sources
Joseph Oesterlé ''Travaux de Ferrero et Washington sur le nombre de classes d'idéaux des corps cyclotomiques'', Séminaire Bourbaki, Nr. 535, 1978/79Lawrence C. Washington, Curriculum Vita
References
External links
Homepage
*
{{DEFAULTSORT:Washington, Lawrence C.
1951 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Modern cryptographers
Number theorists
Johns Hopkins University alumni
Princeton University alumni
University of Maryland, College Park faculty
Fellows of the American Mathematical Society