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, mathematical structure, structure, space, Mathematica ...

, and professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

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 other ...

, he completed his

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

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

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, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

for

Part III Part Three, Part 3 or Part III may refer to: Music * ''Part 3'' (KC and the Sunshine Band album) * ''Part III'' (112 album) (2001 album), R&B album by 112 * " Part Three into Paper Walls", a song by Russell Morris Television * "Part 3" (''True ...

of the

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

. 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 university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

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) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

and then taught at

for three years. In 1983, he moved to

. In 1985, he was struck with a severe case of

multiple sclerosis Multiple sclerosis (MS) is an autoimmune disease resulting in damage to myelinthe insulating covers of nerve cellsin the brain and spinal cord. As a demyelinating disease, MS disrupts the nervous system's ability to Action potential, transmit ...

, 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 colloquially called the "Genius Grant", is a prize awarded annually by the MacArthur Foundation, John D. and Catherine T. MacArthur Foundation to typically between 20 and ...

in 1987. Coleman died on March24, 2014.

Research

He worked primarily in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, with specific interests in

p-adic analysis In mathematics, ''p''-adic analysis is a branch of number theory that studies functions of ''p''-adic numbers. Along with the more classical fields of real and complex analysis, which deal, respectively, with functions on the real and complex ...

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 b ...

, originally proved by

Michel Raynaud Michel Raynaud (; 16 June 1938 – 10 March 2018 Décès de Michel Raynaud
So ...

. Coleman is also known for introducing p-adic Banach spaces into the study of

modular forms In mathematics, a modular form is a holomorphic function on the Upper half-plane#Complex plane, complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the Group action (mathematics), group action of the ...

and discovering important classicality criteria for overconvergent p-adic modular forms. With

Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in ...

, 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 over function fields and managed to fill it in. With

José Felipe Voloch José Felipe Voloch (born 13 February 1963, in Rio de Janeiro) is a Brazilian mathematician who works on number theory and algebraic geometry. He has been a professor at the University of Canterbury since 2016. Career Voloch earned his Ph.D. from ...

, Coleman established an important unchecked compatibility in

Benedict Gross Benedict Hyman Gross (born June 22, 1950) is an American mathematician who is a professor at the University of California, San Diego, the George Vasmer Leverett Professor of Mathematics Emeritus at Harvard University, and former Dean of Harvard C ...

's theory of companion forms. Coleman's effective version of Chabauty's method only applies to curves that satisfy Chabauty's condition. In 2004

Minhyong Kim Minhyong Kim () is a South Korean mathematician who specialises in arithmetic geometry and anabelian geometry. Biography Kim received his PhD at Yale University in 1990 under the supervision of Serge Lang and Barry Mazur, going on to work in a ...

published a far-reaching generalization of Chabauty's method.

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