Robert F Coleman

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Nationality United States Fields Mathematics		Role Mathematician Name Robert Coleman Awards MacArthur Fellowship

Born November 22, 1954 ( 1954-11-22 ) Institutions University of California, Berkeley Alma mater Harvard University Princeton University Doctoral students Matthew Baker Ioan Berbec Roland Dreier Bruce Kaskel Walter Kim Chong Lim Kenneth McMurdy Despina Prapavessi Soogil Seo Lawren Smithline Harvey Stein Pavlos Tzermias Known for p-adic integration Method of Coleman and Chabauty Coleman-Mazur eigencurve overconvergent p-adic modular forms Notable awards MacArthur Fellow (1987) Intel STS (1972) Died March 24, 2014, San Pablo, California, United States Education Princeton University, Harvard University
Doctoral advisor Kenkichi Iwasawa

Robert F. Coleman (November 22 1954 – March 24, 2014) was an American mathematician, and professor at the University of California, Berkeley.

Robert F. Coleman httpsuploadwikimediaorgwikipediacommons11

After graduating from Nova High School, he completed his bachelor's degree at Harvard University in 1976 and subsequently attended Cambridge University for Part III of the mathematical tripos. 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 in 1979 under the advising of Kenkichi Iwasawa. He then had a one-year postdoctoral appointment at the Institute for Advanced Study and then taught at Harvard University for three years. In 1983, he moved to University of California, Berkeley. 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 in 1987.

He worked primarily in number theory, with specific interests in p-adic analysis and arithmetic geometry. 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, originally proved by Raynaud. Coleman is also known for introducing p-adic Banach spaces into the study of modular forms 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 over function fields and managed to fill it in. With José Felipe Voloch, Coleman established an important unchecked compatibility in Dick Gross's theory of companion forms.

Robert Coleman died on March 24, 2014 and is survived by his wife Tessa, sister Rosalind, brother Mark, nephew Jeffrey and niece Elise, and service dog Julep.

Selected works

Coleman, Robert F. (1979), "Division values in local fields.", Invent. Math., 53 (2): 91–116, MR 0560409, doi:10.1007/BF01390028 PhD thesis

Coleman, Robert F. (1985), "Torsion points on curves and p-adic abelian integrals", Ann. of Math., 121: 111–168, MR 0782557, doi:10.2307/1971194

Coleman, Robert F. (1985), "Effective Chabauty", Duke Math. J., 52: 765–770, MR 0808103, doi:10.1215/s0012-7094-85-05240-8

Coleman, Robert F. (1987), "Ramified torsion points on curves", Duke Math. J., 54: 615–640, MR 0899407, doi:10.1215/s0012-7094-87-05425-1

Coleman, Robert F.; de Shalit, Ehud (1988), "p-adic regulators on curves and special values of p-adic L-functions", Invent. Math., 93: 239–266, MR 0948100, doi:10.1007/bf01394332

Coleman, Robert F. (1990), "Manin's proof of the Mordell conjecture over function fields", L'Enseignement Mathématique. Revue Internationale. IIe Série, 36 (3): 393–427, ISSN 0013-8584, MR 1096426

Coleman, Robert F.; Voloch, José Felipe (1992), "Companion forms and Kodaira-Spencer theory", Invent. Math., 110: 263–281, MR 1185584, doi:10.1007/bf01231333

Coleman, Robert F. (1996), "Classical and Overconvergent Modular Forms", Invent. Math., 124: 215–241, MR 1369416, doi:10.1007/s002220050051

Coleman, Robert F. (1997), "p-adic Banach spaces and families of modular forms.", Invent. Math., 127 (3): 417–479, MR 1431135, doi:10.1007/s002220050127

Coleman, R.; Mazur, B. (1998), "The eigencurve", Galois representations in arithmetic algebraic geometry (Durham, 1996) (PDF), London Math. Soc. Lecture Note Ser., 254, Cambridge: Cambridge Univ. Press, pp. 1–113, MR 1696469

Coleman, Robert F. (2003), "Stable maps of curves", Doc. Math., Extra Volume for Kazuya Kato's fiftieth birthday: 217–225, MR 2046600

References

Robert F. Coleman Wikipedia

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