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Enrico Bombieri
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Enrico Bombieri  

100px Enrico Bombieri  
Born  26 November 1940 
Nationality  Italian 
Fields  Mathematics 
Institutions  Institute for Advanced Study 
Alma mater  University of Milan 
Doctoral advisor  Template:If empty 
Known for 
Large sieve method in analytic number theory BombieriLang conjecture Bombieri norm Bombieri–Vinogradov theorem "Heights" in Diophantine geometry Siegel's lemma for bases (Bombieri–Vaaler) Partial differential equations Bombieri–Friedlander–Iwaniec theorem 
Notable awards 
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 
Enrico Bombieri (born 26 November 1940 in Milan, Italy) is a mathematician, known for his work in analytic number theory, algebraic geometry, univalent functions, theory of several complex variables, partial differential equations of minimal surfaces, and the theory of finite groups. He won a Fields Medal in 1974.^{[5]}
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 USA, 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's research in number theory, algebraic geometry, and mathematical analysis have earned him many international prizes — a Fields Medal in 1974 and the Balzan Prize in 1980. In 2010 he received the King Faisal International Prize (jointly with Terence Tao).^{[6]}^{[7]} He is a member, or foreign member, of several learned academies, including the French Academy of Sciences (elected 1984), the United States National Academy of Sciences (elected 1996), and the Accademia Nazionale dei Lincei (elected 1976).^{[8]} In 2002 he was made Cavaliere di Gran Croce al Merito della Repubblica Italiana.^{[9]}
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 stillunproved generalized Riemann hypothesis.
In 1969 Bombieri, De Giorgi, and Giusti solved Bernstein's problem.^{[10]}
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]}
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 peerreviewing extraordinarily complicated manuscripts (like the paper of Per Enflo on the invariant subspace problem).
Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.
See also
Notes
 ↑ Site of Caccioppoli Prize
 ↑ Premio Pitagora 2006 Invalid language code.
 ↑ Joseph L. Doob Prize
 ↑ "2008 Doob Prize" (PDF). Notices of the AMS 55 (4): 503–504. April 2008.
 ↑ Proceedings of the International Congress of Mathematicians, 1974
 ↑ King Faisal Foundation,  retrieved 20100111.
 ↑ "Bombieri and Tao Receive King Faisal Prize" (PDF). Notices of the AMS 57 (5): 642–643. May 2010.
 ↑ Scheda socio, from the website of Accademia dei Lincei (elected 1976)
 ↑ Torno Armando (28 May 2002). "BOMBIERI Il re dei numeri che ha conquistato il mondo". Corriere della Serra (in italiano). p. 35.
 ↑ Bombieri, Enrico; De Giorgi, Ennio; Giusti, Enrico (1969), "Minimal cones and the Bernstein problem", Inventiones Mathematicae 7: 243–268, ISSN 00209910, MR 0250205, doi:10.1007/BF01404309
 ↑ E. Bombieri, "The asymptotic sieve", Mem. Acad. Naz. dei XL, 1/2 (1976) 243–269.
 ↑ Bombieri, E. (1980). "Thompson's problem σ^{2}=3. Appendices by A. Odlyzko and D. Hunt". Invent. Math. 58 (1): 77–100. doi:10.1007/bf01402275. (This paper completed a line of research initiated by the Walter theorem.)
References
 Bombieri, E.; Mueller, J. "On effective measures of irrationality for <math>{\scriptscriptstyle\sqrt[r]{a/b".</math> and related numbersjournal = Journal für die reine und angewandte Mathematikvolume = 342year = 1983pages = 173–196}}
 Bombieri, E.; Vaaler, J. (Feb 1983). "On Siegel's lemma". Inventiones Mathematicae 73 (1): 11–32. doi:10.1007/BF01393823.
 E. Bombieri, Le Grand Crible dans la Théorie Analytique des Nombres (Seconde Édition). Astérisque 18, Paris 1987.
 B. Beauzamy, E. Bombieri, P. Enflo and H. L. Montgomery. "Product of polynomials in many variables", Journal of Number Theory, pages 219–245, 1990.
 Enrico Bombieri and Walter Gubler (2006). Heights in Diophantine Geometry. Cambridge U. P.
External links
 Enrico Bombieri at the Mathematics Genealogy Project
 O'Connor, John J.; Robertson, Edmund F., "Enrico Bombieri", MacTutor History of Mathematics archive, University of St Andrews.
 Enrico Bombieri, Institute for Advanced Study
 Lista delle pubblicazioni di Enrico Bombieri, University of Pisa

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