Enrico Bombieri

Enrico Bombieri (2006)

Enrico Bombieri (born November 26, 1940 in Milan ) is an Italian mathematician . He works at the Institute for Advanced Study in Princeton , New Jersey . He is known for his work in the fields of number theory , algebraic geometry , analysis and group theory .

In 1974 he was awarded the Fields Medal (plenary lecture: Variational problems and elliptic equations ).

Life

Bombieri studied in Milan , where he obtained his doctorate in 1963 with Giovanni Ricci , and in Cambridge with Harold Davenport . He taught from 1966 at the Normal Scuola Superiore di Pisa and Sassari before 1977 in the United States to the Institute for Advanced Study in Princeton went where he is currently "IBM John von Neumann" -Professor of Mathematics.

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The Bombieri theorem (or "Bombieri's mean value theorem" or " Theorem of Bombieri and Winogradow ", after Bombieri and Askold Ivanovich Winogradow ) is an extension of Dirichlet's prime number theorem about prime numbers in arithmetic sequences . It was found by him through an application of the "Great Sieve", which he developed further, in analytical number theory (originally by Juri Linnik and Alfréd Rényi ).

From the mid-1960s he turned to the theory of minimal surfaces or, more generally, minimal submanifolds in higher-dimensional Euclidean spaces, partly in collaboration with Ennio de Giorgi and Enrico Giusti . With these he succeeded in 1969 in the complete solution of the Bernstein problem (named after Sergei Bernstein , who treated the case of two dimensions in Bernstein's theorem ) by showing that Bernstein's theorem no longer applies in 8 or more dimensions.

In algebraic geometry, he dealt with the classification of algebraic surfaces in characteristics , where he partly collaborated with David Mumford . ${\displaystyle p}$

He also dealt ( Inventiones Mathematicae 1967/1968) with the local form of Bieberbach's conjecture for simple functions in the unit circle.

Awards and memberships

In 1966 he received the Premio Caccioppoli , in 1974 the Fields Medal , in 1976 the Antonio Feltrinelli Prize and in 1980 the Balzan Prize for Mathematics. In 2008 he received the Joseph L. Doob Prize of the American Mathematical Society for the book Heights in Diophantine Geometry with Walter Gubler . In 2010 he was awarded the King Faisal International Prize together with Terence Tao and in 2020 the Crafoord Prize in Mathematics.

He is a member of the Accademia Nazionale delle Scienze , the Accademia dei XL , the Academia Europaea , the Académie des Sciences (since 1980), the Institut de France, the National Academy of Sciences (since 1996), the Royal Swedish Academy of Sciences and since 1979 member of the American Academy of Arts and Sciences . In 2002 he became Cavaliere di Gran Croce al Merito della Repubblica.

In 2005/06 and 2006/07 he was on the Abel Prize Committee .

Fonts

• On the large sieve, Mathematika, Volume 12, 1965, pp. 201-225
• with Harold Davenport : Small differences between prime numbers, Proc Roy Soc Ser A, Volume 293, 1966, pp. 1-18
• On exponential sums in finite fields, Am. J. Math., Vol. 88, 1966, pp. 71-105
• On Galois coverings over finite fields, Proc Internat Colloq Alg Geom, Madrid, 1965, Madrid: Inst Jorge Juan del CSIC IMU, 1966, pp. 23-30
• with H. Davenport: On two problems of Mordell, Am J Math, Volume 88, 1966, pp. 61-70
• with Peter Swinnerton-Dyer : On the local zeta function of a cubic threefold, Ann Scuola Norm Sup Pisa (3), Volume 21, 1967, pp. 1-29
• On the local maximum property of the Koebe function, Inv. Math., Vol. 4, 1967, pp. 26-27
• A geometric approach to some coefficient inequalities for univalent functions, Ann. Scuola Normale Superiore Pisa, Volume 22, 1968, pp. 377-397
• with Ennio di Giorgi, Enrico Giusti: Minimal cones and the Bernstein problem , Inventiones Mathematicae, Volume 7, 1969, pp. 243-268
• with Serge Lang : Analytic subgroups of group varieties, Inv. Math., Vol. 11, 1970, pp. 1-14
• Canonical models of surfaces of general type, Pub. Math. IHES, Vol. 42, 1973, pp. 171-219
• with Dale Husemoller : Classification and embeddings of surfaces, Proc. Symp. Pure Math., Vol. 29, 1975, pp. 329-420
• On twin almost primes, Acta Arithmeticae, Vol. 28, 1975, pp. 177-193
• with Wolfgang Schmidt : Simultaneous approximations of algebraic numbers, Lecture notes in mathematics 317, 1973, pp. 1–20
• with David Mumford: Enriques Classification of surfaces in char p, part 2, in: Complex Analysis and Algebraic Geometry, Cambridge UP 1977, pp. 23-42, part 3, Inventiones Mathematicae, Volume 35, 1976, pp. 197-232
• with J. Vaaler: On Siegel's lemma, Inventiones Mathematicae, Volume 73, 1983, pp. 11-32
• Le Grand Crible dans la Théorie Analytique des Nombres (Seconde Édition). Astérisque 18, 1974
• with B. Beauzamy, Per Enflo , Hugh Montgomery : Product of polynomials in many variables, Journal of Number Theory, Volume 36, 1990, pp. 219-245
• with Walter Gubler: Heights in Diophantine Geometry, Cambridge University Press 2006

Web links

• John J. O'Connor, Edmund F. Robertson :  Enrico Bombieri. In: MacTutor History of Mathematics archive .
• King Faisal Foundation
• Website at the IAS

Individual evidence

1. ↑ Enrico Bombieri in the Mathematics Genealogy Project (English)
2. ^ Bernstein Problem , Encyclopedia of Mathematics, Springer
3. ↑ King Faisal Foundation , - accessed January 12, 2010.
4. ↑ Crafoord Prize 2020
5. ^ Abel Committee