Bernard Morris Dwork (May 27, 1923 – May 9, 1998) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, known for his application of ''p''-adic analysis to

local zeta function In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as :Z(V, s) = \exp\left(\sum_^\infty \frac (q^)^m\right) where is a non-singular -dimensional projective algebr ...

s, and in particular for a proof of the first part of the

Weil conjectures In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory. ...

: the rationality of the zeta-function of a

variety Variety may refer to: Arts and entertainment Entertainment formats * Variety (radio) * Variety show, in theater and television Films * ''Variety'' (1925 film), a German silent film directed by Ewald Andre Dupont * ''Variety'' (1935 film), ...

over a

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...

. The general theme of Dwork's research was ''p''-adic

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

and ''p''-adic

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...

s. He published two papers under the pseudonym Maurizio Boyarsky.

Career

Dwork received his Ph.D. at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

in 1954 under direction of

Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing ...

(his formal advisor was John Tate);

Nick Katz Nicholas Michael Katz (born December 7, 1943) is an American mathematician, working in arithmetic geometry, particularly on ''p''-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at P ...

was one of his students.. For his proof of the first part of the Weil conjectures, Dwork received (together with

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 ...

) the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...

in 1962.Memorial article
– by

and John Tate. He received a

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

1964 Events January * January 1 – The Federation of Rhodesia and Nyasaland is dissolved. * January 5 - In the first meeting between leaders of the Roman Catholic and Orthodox churches since the fifteenth century, Pope Paul VI and Patriarc ...

Personal life

Dwork is the father of

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus ( ...

Cynthia Dwork, who received the

Dijkstra Prize The Edsger W. Dijkstra Paper Prize in Distributed Computing is given for outstanding papers on the principles of distributed computing, whose significance and impact on the theory and/or practice of distributed computing has been evident for at lea ...

and is now continuing as a Radcliffe Scholar at Harvard University. His other daughter, historian Deborah Dwork, received a Guggenheim Fellowship in

1993 File:1993 Events Collage.png, From left, clockwise: The Oslo I Accord is signed in an attempt to resolve the Israeli–Palestinian conflict; The Russian White House is shelled during the 1993 Russian constitutional crisis; Czechoslovakia is peace ...

. Additionally, his son Andrew Dwork works as a Professor of Clinical Pathology and Cell Biology (in Psychiatry), at Columbia University, focusing his work on neuropathology of psychiatric disorders.

References

{{DEFAULTSORT:Dwork, Bernard 1923 births 1998 deaths Algebraic geometers 20th-century American mathematicians Institute for Advanced Study visiting scholars Columbia University alumni Princeton University faculty

Career

Personal life

See also

References