Lawrence Clinton Washington (born 1951,

Vermont Vermont () is a state in the northeast New England region of the United States. Vermont is bordered by the states of Massachusetts to the south, New Hampshire to the east, and New York to the west, and the Canadian province of Quebec to ...

) is an American mathematician 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 ...

who specializes in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

Biography

Washington studied at

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

, where in 1971 he received his B.A. and master's degree. In 1974 he earned his PhD at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

under

Kenkichi Iwasawa Kenkichi Iwasawa ( ''Iwasawa Kenkichi'', September 11, 1917 – October 26, 1998) was a Japanese mathematician who is known for his influence on algebraic number theory. Biography Iwasawa was born in Shinshuku-mura, a town near Kiryū, in Gun ...

with thesis ''Class numbers and

Z_p

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

, 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 The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

(1996), and MSRI (1986/87), as well as at the

University of Perugia University of Perugia (Italian ''Università degli Studi di Perugia'') is a public-owned university based in Perugia, Italy. It was founded in 1308, as attested by the Bull issued by Pope Clement V certifying the birth of the Studium Generale. Th ...

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 The State University of Campinas ( pt, Universidade Estadual de Campinas), commonly called Unicamp, is a public research university in the state of São Paulo, Brazil. Unicamp is consistently ranked among the top universities in Brazil and Latin ...

. In 1979–1981 he was a

Sloan Fellow The Sloan Fellows program is the world's first mid-career and senior career master's degree in general management and leadership. It was initially supported by a grant from Alfred P. Sloan, the late CEO of General Motors, to his alma mater, MIT ...

Recognition

He was named to the 2023 class of Fellows 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, ...

, "for contributions to number theory, especially cyclotomic fields, and for mentoring at all levels".

Research

Washington wrote a standard work on

cyclotomic field In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to , the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of th ...

s. He also worked on

p-adic In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension ...

L-function In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give ris ...

s. 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 In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the ea ...

, Cohen- Lenstra heuristics, and

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s and their applications to

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

. In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of

, that the

\mu

-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 μ_p 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 Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard s ...

, 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