Ken Ribet

Ken Ribet
Kenneth A. Ribet in 2013
Born (1948-06-28) June 28, 1948 (age 76)
NationalityAmerican
Alma materBrown University (BA, MA)
Harvard University (PhD)
Known forRibet's lemma
Ribet's theorem
Herbrand–Ribet theorem
Awards
Scientific career
FieldsMathematics
InstitutionsPrinceton University
University of California, Berkeley
Thesis Galois action on division points of abelian varieties with real multiplications  (1973)
Doctoral advisorJohn Tate
Doctoral studentsFrank Calegari
Samit Dasgupta
Bjorn Poonen

Kenneth Alan Ribet (/ˈrɪbɪt/; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's Last Theorem, as well as for his service as President of the American Mathematical Society from 2017 to 2019. He is currently a professor of mathematics at the University of California, Berkeley.

Early life and education

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Kenneth Ribet was born in Brooklyn, New York to parents David Ribet and Pearl Ribet, both Jewish, on June 28, 1948.[1] As a student at Far Rockaway High School, Ribet was on a competitive mathematics team, but his first field of study was chemistry.[2]

Ribet earned his bachelor's degree and master's degree from Brown University in 1969.[3][4] In 1973, Ribet received his Ph.D. from Harvard University under the supervision of John Tate.[3][5][4]

Career

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After receiving his doctoral degree, Ribet taught at Princeton University for three years before spending two years doing research in Paris.[3] In 1978, Ribet joined the Department of Mathematics at the University of California, Berkeley, where he served three separate terms as supervisor of the department's graduate program, supervisor of the department's undergraduate program, and supervisor of the department's development.[3]

Ribet has served as an editor for several mathematics journals, a book series editor for the Cambridge University Press, and a book series editor for Springer.[3] He also served on the United States National Committee for Mathematics, representing the United States at the International Mathematical Union, and was the Chair of the Mathematics section of the National Academy of Sciences.[3]

From February 1, 2017 to January 31, 2019, Ribet was President of the American Mathematical Society.[6]

Research

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Further information: Ribet's theorem

Ribet's contributions in number theory and algebraic geometry were described by Benedict Gross and Barry Mazur as being "key to our understanding of the connections between the theory of modular forms and the ℓ-adic representations of the absolute Galois group of the field of rational numbers."[3]

Ribet is credited with paving the way towards Andrew Wiles's proof of Fermat's Last Theorem. In 1986, Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed.[7] An earlier theorem of Ribet's, the Herbrand–Ribet theorem, is the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers and is also related to Fermat's Last Theorem.[8][9][10][11]

Awards and honors

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Ribet received the Fermat Prize in 1989 jointly with Abbas Bahri.[6][3] He was elected to the American Academy of Arts and Sciences in 1997 and the National Academy of Sciences in 2000.[6][3][4] In 2012, he became a Fellow of the American Mathematical Society.[12][6] In 2017, Ribet received the Brouwer Medal.[13]

In 1988, Ribet was inducted as a vigneron d'honneur by the Jurade de Saint-Émilion.[4] In 1998, Ribet received an honorary doctorate from Brown University.[4]

Personal life

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Ribet is married to statistician Lisa Goldberg.[14]

References

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  1. ^ "Jewish Mathematicians".
  2. ^ Chapey, Dr. Geraldine. "Chatting with Chapey: Weber and Ribet Honored", The Wave, October 21, 2005. Accessed September 28, 2018. "Speaking of successful professionals, Kenneth Ribet is a world renowned scholar.... He is a proud graduate of P.S. 114, J.H.S. 210 and Far Rockaway High School."
  3. ^ a b c d e f g h i Gross, Benedict; Mazur, Barry (September 2015). "Nomination of Kenneth Ribet" (PDF). Notices of the American Mathematical Society. 62 (8): 931–956.
  4. ^ a b c d e "Kenneth A. Ribet". Institute for Advanced Study. 9 December 2019. Retrieved August 4, 2020.
  5. ^ Ken Ribet at the Mathematics Genealogy Project
  6. ^ a b c d "AMS President #64 Kenneth A. Ribet (2017–2018)". American Mathematical Society. Retrieved August 4, 2020.
  7. ^ Ribet, Ken (1990). "On modular representations of Gal(Q/Q) arising from modular forms" (PDF). Inventiones Mathematicae. 100 (2): 431–476. Bibcode:1990InMat.100..431R. doi:10.1007/BF01231195. MR 1047143. S2CID 120614740.
  8. ^ Ribet, Ken (1976). "A modular construction of unramified p-extensions of (μp)". Inv. Math. 34 (3): 151–162. doi:10.1007/bf01403065. S2CID 120199454.
  9. ^ Washington, Lawrence C. (1997). Introduction to Cyclotomic Fields (Second ed.). New York: Springer-Verlag. ISBN 0-387-94762-0.
  10. ^ Mazur, Barry & Wiles, Andrew (1984). "Class Fields of Abelian Extension of ". Inv. Math. 76 (2): 179–330. Bibcode:1984InMat..76..179M. doi:10.1007/bf01388599. S2CID 122576427.
  11. ^ Coates, John; Sujatha, R. (2006). Cyclotomic Fields and Zeta Values. Springer Monographs in Mathematics. Springer-Verlag. pp. 3–4. ISBN 3-540-33068-2. Zbl 1100.11002.
  12. ^ List of Fellows of the American Mathematical Society, retrieved 2013-07-07.
  13. ^ "2017 Brouwer Medal to Kenneth Ribet". European Mathematical Society. 2 March 2017. Retrieved August 4, 2020.
  14. ^ Jackson, Allyn (March 2017). "Interview with New AMS President Kenneth A. Ribet" (PDF). Notices of the American Mathematical Society. 64 (3): 229–232. doi:10.1090/noti1488.
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