ⓘ Enrico Bombieri

                                     

ⓘ Enrico Bombieri

Enrico Bombieri is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. He won a Fields Medal in 1974. Bombieri is currently Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.

                                     

1. 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 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.

                                     

2. Research

The Bombieri–Vinogradov theorem is one of the major applications of the large sieve method. It improves Dirichlets 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 Bernsteins problem.

In 1976, Bombieri developed the technique known as the "asymptotic sieve". 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.

                                     

3. Awards

Bombieris 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. 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 French Academy of Sciences elected 1984, the United States National Academy of Sciences elected 1996, and the Accademia Nazionale dei Lincei elected 1976. In 2002 he was made Cavaliere di Gran Croce al Merito della Repubblica Italiana. In 2010 he received the King Faisal International Prize jointly with Terence Tao. and in 2020 he was awarded the Crafoord Prize in Mathematics.

                                     

4. 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.

With his powder-blue shirt open at the neck, khaki pants and running shoes, he might pass for an Italian film director at Cannes. Married with a grown daughter, he is a gourmet cook and a serious painter: He carries his paints and brushes with him whenever he travels. Still, mathematics never seems far from his mind. In a recent painting, Bombieri, a one-time member of the Cambridge University chess team, depicts a giant chessboard by a lake. Hes placed the pieces to reflect a critical point in the historic match in which IBMs chess-playing computers, Deep Blue, beat Garry Kasparov.

                                     
  • geometry, the Bombieri Lang conjecture is an unproved conjecture about the rational points on an algebraic surface, named after Enrico Bombieri and Serge
  • 1961 and the Bombieri Vinogradov theorem is a refinement of Barban s result. The Bombieri Vinogradov theorem is named after Enrico Bombieri and A. I. Vinogradov
  • One of the most famous results of Giusti, is the one obtained with Enrico Bombieri and Ennio De Giorgi, concerning the minimality of Simons cones, and
  • his collaborations with other well - known number theorists, including Enrico Bombieri William Duke, Andrew Granville, and especially Henryk Iwaniec. In
  • coach Enrico Bombieri born 1940 Italian mathematician Enrico Boselli born 1957 Italian politician Enrico Brizzi born 1974 Italian writer Enrico Cardoso
  • determinant method was developed by Enrico Bombieri and Jonathan Pila in 1989. In its original context, Bombieri and Pila s results applied only to A
  • Schmidt extended Stepanov s methods to prove the general result, and Enrico Bombieri succeeded in using the work of Stepanov and Schmidt to give a substantially
  • in polyhedra, Undergraduate Texts in Mathematics, Springer, 2007. Enrico Bombieri Vaaler, J. Feb 1983 On Siegel s lemma Inventiones Mathematicae
  • University of Pisa 1964 Emilio Gagliardo University of Genova 1966 Enrico Bombieri University of Pisa 1968 Mario Miranda University of Pisa 1970 Claudio
  • criterion is named after Xian - Jin Li, who presented it in 1997. In 1999, Enrico Bombieri and Jeffrey C. Lagarias provided a generalization, showing that Li s