Enrico Bombieri Explained

Enrico Bombieri
Birth Date:26 November 1940
Birth Place:Milan, Italy
Field:Mathematics
Work Institutions:Institute for Advanced Study
Alma Mater:University of Milan
Trinity College, Cambridge
Doctoral Advisor:Giovanni Ricci
Doctoral Students:Umberto Zannier
Prizes:1966, Caccioppoli Prize[1]
1974, Fields Medal
1976, Feltrinelli Prize
1980, Balzan Prize
2006, Pythagoras Prize[2]
2008, Joseph L. Doob Prize[3] [4]
2010, King Faisal International Prize
2020, Crafoord Prize

Enrico Bombieri (born 26 November 1940) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory.[5] Bombieri is currently Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.[6] Bombieri won the Fields Medal in 1974[5] for his contributions to large sieve mathematics, conceptualized by Linnick 1941,[7] [8] and its application to the distribution of prime numbers.[9]

Career

Bombieri published his first mathematical paper in 1957 when he was 16 years old. In 1963 at age 22 he earned his first degree (Laurea) in mathematics from the Università degli Studi di Milano under the supervision of Giovanni Ricci and then studied at Trinity College, Cambridge, with Harold Davenport.

Bombieri was an assistant professor (1963–1965) and then a full professor (1965–1966) at the Università di Cagliari, at the Università di Pisa in 1966–1974, and then at the Scuola Normale Superiore di Pisa in 1974–1977. From Pisa, he emigrated in 1977 to the United States, where he became a professor at the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey. In 2011 he became professor emeritus.

Bombieri is also known for his pro bono service on behalf of the mathematics profession, e.g. for serving on external review boards and for peer-reviewing extraordinarily complicated manuscripts (like the paper of Per Enflo on the invariant subspace problem).[10]

Research

The Bombieri–Vinogradov theorem is one of the major applications of the large sieve method. It improves Dirichlet's theorem on prime numbers in arithmetic progressions, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case. This result can sometimes substitute for the still-unproved generalized Riemann hypothesis.

In 1969 Bombieri, De Giorgi, and Giusti solved Bernstein's problem.

In 1976, Bombieri developed the technique known as the "asymptotic sieve".[11] In 1980 he supplied the completion of the proof of the uniqueness of finite groups of Ree type in characteristic 3; at the time of its publication, it was one of the missing steps in the classification of finite simple groups.[12]

Awards

Bombieri's research in number theory, algebraic geometry, and mathematical analysis has earned him many international prizes — a Fields Medal in 1974 and the Balzan Prize in 1980. He was a plenary speaker at the International Congress of Mathematicians in 1974 at Vancouver. He is a member, or foreign member, of several learned academies, including the Accademia Nazionale dei Lincei (elected 1976), the French Academy of Sciences (elected 1984), and the United States National Academy of Sciences (elected 1996).[13] In 2002 he was made Cavaliere di Gran Croce al Merito della Repubblica Italiana.[14] In 2010 he received the King Faisal International Prize (jointly with Terence Tao).[15] [16] and in 2020 he was awarded the Crafoord Prize in Mathematics.[17]

Other interests

Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.[18]

Selected publications

Sole

Joint

See also

Sources

External links

Notes and References

  1. Web site: Site of Caccioppoli Prize. 2011-12-31. 2019-05-14. https://web.archive.org/web/20190514091912/http://umi.dm.unibo.it/caccioppoli/index-en.html. dead.
  2. http://www.math.it/eventi/premiopitagora_06.htm Premio Pitagora 2006
  3. Web site: Joseph L. Doob Prize.
  4. 2008 Doob Prize. Notices of the AMS. April 2008. 55. 4. 503–504.
  5. Web site: Proceedings of the International Congress of Mathematicians, 1974 . https://web.archive.org/web/20131113045006/http://www.mathunion.org/ICM/ICM1974.1/ICM1974.1.ocr.pdf . 13 November 2013 . dead.
  6. Web site: Enrico Bombieri. Institute for Advanced Study. en. 2019-08-07.
  7. Web site: Notes on the large sieve. Jameson. GJO. www.maths.lancs.ac.uk (University of Lancaster). 2 July 2021.
  8. Book: The Large Sieve and its Applications Arithmetic Geometry, Random Walks and Discrete Groups Part of Cambridge Tracts in Mathematics AUTHOR: E. Kowalski. synopsis of text by Cambridge University Press. Swiss Federal University (ETH), Zürich (May 2008): www.cambridge.org (Cambridge University Press). 9780521888516.
  9. Web site: Enrico Bombieri PROFESSOR EMERITUS School of Mathematics Number Theory. www.ias.edu (Institute for Advanced Study). 9 December 2019. 2 July 2021.
  10. Enflo . Per . On the invariant subspace problem for Banach spaces . Acta Mathematica . 158 . 0 . 1987 . 0001-5962 . 10.1007/BF02392260 . 213–313.
  11. E. Bombieri, "The asymptotic sieve", Mem. Acad. Naz. dei XL, 1/2 (1976) 243–269.
  12. Bombieri, E.. Thompson's problem σ2=3. Appendices by A. Odlyzko and D. Hunt. Invent. Math.. 58. 1. 1980. 77–100. 10.1007/bf01402275. 122867511. (This paper completed a line of research initiated by the Walter theorem.)
  13. http://www.lincei.it/modules.php?name=Soci&file=scheda&func=Soci_scheda&Id=438 Scheda socio
  14. News: Torno Armando. BOMBIERI Il re dei numeri che ha conquistato il mondo. Corriere della Sera. 28 May 2002. 35. it.
  15. http://www.kff.com/ King Faisal Foundation
  16. Bombieri and Tao Receive King Faisal Prize. Notices of the AMS. May 2010. 57. 5. 642–643.
  17. Web site: Crafoord Prize 2020. 29 January 2020.
  18. http://www.italyonthisday.com/2018/11/enrico-bombieri-mathematician.html Bombieri – Mathematician