Henryk Iwaniec

Henryk Iwaniec (born October 9, 1947 in Elbląg in Poland ) is a Polish-American mathematician who deals with analytical number theory.

Henryk Iwaniec

Life

Iwaniec studied at the University of Warsaw , where he twice won the Marcinkiewicz Prize in the late 1960s. In 1971 he completed his studies and was the following year when Andrzej Schinzel doctorate . After that he was at the Institute of Mathematics of the Polish Academy of Sciences. In 1976 he completed his habilitation. In 1976/77 he was at the Scuola Normale Superiore in Pisa with a scholarship from the Accademia dei Lincei and in 1979/80 at the University of Bordeaux. In 1983 he became a professor and corresponding member of the Polish Academy of Sciences. From 1983/84 to 1986 he was at the Institute for Advanced Study (IAS) in Princeton and in 1984 at the University of Michigan in Ann Arbor and visiting professor in Boulder . Since 1987 he has been a professor at Rutgers University . In 1999/2000 he was visiting professor at the IAS.

He is the twin brother of Tadeusz Iwaniec .

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Iwaniec has made significant advances in analytical number theory. In 1997, together with John Friedlander, he proved, by using the asymptotic sieve by Enrico Bombieri , which they refined , that there are an infinite number of prime numbers of the form ( natural numbers) - the Bombieri-Friedlander-Iwaniec theorem. In the 19th century, one of the founders of analytical number theory, Peter Gustav Lejeune Dirichlet , had shown that there are an infinite number of prime numbers in linear sequences of the form ( coprime to one another), and also in other subsets of natural numbers that are relatively "close" (i.e. containing many composite numbers in addition to prime numbers), similar theorems were proven. In the problem examined by Iwaniec and Friedlander, a breakthrough was achieved for the first time with a relatively “thin” subset of the natural numbers. ${\displaystyle a^{2}+b^{4}}$ ${\displaystyle a,b}$ ${\displaystyle a+d,a+2d,a+3d,a+4d,\ldots }$ ${\displaystyle a,d}$

Iwaniec also solved Juri Linnik's problem in the geometry of numbers, which is the uniform distribution of grid points on two-dimensional spheres around the origin if the radius increases. Another field of work of Iwaniec is the analytical theory of automorphic forms for linear groups and their functions, in which he also partly worked with Friedlander as well as with William Duke and Peter Sarnak . ${\displaystyle GL(2)}$ ${\displaystyle L}$

With Jean-Marc Deshouillers , he wrote an influential work in 1982 on a generalization of the trace formula by Kuznetzow, which connects Kloosterman sums with sums of Fourier coefficients of modular forms. With Étienne Fouvry , he applied the method in 1983 to prove a theorem about prime numbers in arithmetic sequences that went beyond the Bombieri-Vinogradov theorem and which he further tightened with Friedlander and Bombieri.

Honors, miscellaneous

In 1978 he received the Polish State Prize and in 1996 the Sierpinski Medal. In 2001 he received the Ostrowski Prize and in 2002 the Cole Prize for Number Theory. In 1995 he was admitted to the American Academy of Arts and Sciences , and in 2006 to the National Academy of Sciences . In 1978 ( Sieve methods ) and 1986 ( Spectral theory of automorphic functions and recent developments in analytic number theory ) he was invited speaker at the International Congress of Mathematicians (ICM) and gave a plenary lecture there in 2006 ( Prime Numbers and L-functions ). In the same year he became an honorary citizen of his hometown Elbląg. In 2011 he received the Leroy P. Steele Prize . In 2012 he was elected an external member of the Finnish Academy of Sciences . He is a Fellow of the American Mathematical Society and an external member of the Polish Academy of Learning in Krakow . In 2015 he and Gerd Faltings received the Shaw Prize for Mathematics. Iwaniec was also awarded the Stefan Banach Medal in 2015. For 2017 he was awarded the AMS Joseph L. Doob Prize together with John Friedlander for their book on sieving methods (Opera de Cribro, American Mathematical Society, 2010).

He is a citizen of the USA .

His PhD students include Emmanuel Kowalski and Étienne Fouvry .

Fonts

• Topics in Classical Automorphic Forms (= Graduate Studies in Mathematics. 17). American Mathematical Society, Providence RI 1997, ISBN 0-8218-0777-3 .
• Introduction to the Spectral Theory of Automorphic Forms. Revista Matemática Iberoamericana, Madrid 1995 (2nd edition as: Spectral Methods of Automorphic Forms (= Graduate Studies in Mathematics. 53). American Mathematical Society, Providence RI 2002, ISBN 0-8218-3160-7 ).
• with Emmanuel Kowalski : Analytic Number Theory (= American Mathematical Society. Colloquium Publications. 53). American Mathematical Society, Providence RI 2004, ISBN 0-8218-3633-1 .
• with John Friedlander : Opera de Cribro (= American Mathematical Society. Colloquium Publications. 57). American Mathematical Society, Providence RI 2010, ISBN 978-0-8218-4970-5 (sieving methods).
• Lectures on the Riemann Zeta Function (= American Mathematical Society. University Lecture Series. 62). American Mathematical Society, Providence RI 2014, ISBN 978-1-4704-1851-9 .

Web links

• Henryk Iwaniec in the Mathematics Genealogy Project (English)
• The AMS as evidence of Friedlander and Iwaniec ( Memento of November 10, 2007 in the Internet Archive )

Individual evidence

1. ↑ You overcome the so-called parity problem of this sieve. Friedlander, Iwaniec: Asymptotic Sieve for Primes. In: Annals of Mathematics . Vol. 148, No. 3, 1998, pp. 1041-1065, doi : 10.2307 / 121035 . Using parity sensitive sieve to count prime values ​​of a polynomial. In: Proceedings of the National Academy of Sciences of the United States of America . Vol. 94, No. 4, 1997, pp. 1054-1058, doi : 10.1073 / pnas.94.4.1054 .
2. ^ Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize (PDF; 63 kB)
3. ^ Shaw Prize 2015 - Mathematics
4. ↑ 2017 AMS Joseph L. Doob Prize