Robert Frederick Coleman (November22 1954March24, 2014) 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, structure, space, models, and change. History On ...

, and professor 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 ...

Biography

After graduating from

Nova High School Nova High School is a public high school located in Davie, Florida and is part of the Broward County Public Schools district. It is one of four schools that comprise the Nova Center for Applied Research and Professional Development, the others ...

, he completed his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

in 1976 and subsequently attended

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...

for

Part III ''Part III'' is the third studio album by American R&B group 112. It was released by Bad Boy Records on March 20, 2001 in the United States. Unlike the previous releases, the album is described as having edgier, techno-flavored jams, resulting ...

of the

mathematical tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos examined at the University. Origin In its classical nineteenth-century form, the tripos was ...

. While there John H. Coates provided him with a problem for his doctoral thesis ("Division Values in Local Fields"), which he completed at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

in 1979 under the advising of

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 Gunm ...

. He then had a one-year postdoctoral appointment at 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 schola ...

and then taught at

for three years. In 1983, he moved to

. In 1985, he was struck with a severe case of multiple sclerosis, in which he lost the use of his legs. Despite this, he remained an active faculty member until his retirement in 2013. He was awarded a

MacArthur fellowship The MacArthur Fellows Program, also known as the MacArthur Fellowship and commonly but unofficially known as the "Genius Grant", is a prize awarded annually by the John D. and Catherine T. MacArthur Foundation typically to between 20 and 30 indi ...

in 1987. Coleman died on March24, 2014.

Research

He worked primarily 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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

, with specific interests in p-adic analysis and

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

. In particular, he developed a theory of p-adic integration analogous to the classical complex theory of abelian integrals. Applications of Coleman integration include an effective version of Chabauty's theorem concerning rational points on curves and a new proof of the

Manin-Mumford conjecture In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has ...

, originally proved by Raynaud. Coleman is also known for introducing p-adic Banach spaces into the study of

modular forms In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of ...

and discovering important classicality criteria for overconvergent p-adic modular forms. With Barry Mazur, he introduced the eigencurve and established some of its fundamental properties. In 1990, Coleman found a gap in Manin's proof of the

Mordell conjecture Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

over function fields and managed to fill it in. With José Felipe Voloch, Coleman established an important unchecked compatibility in Benedict Gross's theory of companion forms.

Selected works

* PhD thesis * * * * * * * * * *

References

External links

Robert Coleman's Home Page
*
Robert F. Coleman's facebook pageMatt Baker's blog: Robert F. Coleman 1954-2014
{{DEFAULTSORT:Coleman, Robert F 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni University of California, Berkeley College of Letters and Science faculty MacArthur Fellows 1954 births 2014 deaths