Don Zagier

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Don Zagier 2014

Don Bernard Zagier (born June 29, 1951 in Heidelberg ) is an American mathematician . From 2000 to 2014 he was a professor at the Collège de France in Paris. From 1995 to June 2019 he was one of the directors of the Max Planck Institute for Mathematics in Bonn . His main areas of work are number theory , theory of modular forms and connections to topology .

biography

Zagier was born in 1951 in Heidelberg to American parents and grew up in the USA. He passed his Abitur at the age of 13. He studied mathematics and physics at MIT and became a Putnam Fellow in 1967 - at the age of 16 (he won first prize in the Mathematics Olympiad the year before). In 1968 he received his BA, then went to Oxford University and Bonn University , where he did his doctorate under Friedrich Hirzebruch at the age of 20 (officially in Oxford). After two years of residence at the ETH Zurich and the IHES in Bures-sur-Yvette, near Paris, he came in 1974 to Bonn, habilitated in 1975 and in 1976 was Germany's youngest professor. In 1984 he was appointed Scientific Member of the Max Planck Society at the Max Planck Institute for Mathematics in Bonn, where he was appointed Director in 1995. From 1979 to 1990 he was also a professor at the University of Maryland and then until 2001 professor at the University of Utrecht . From 2000 to 2014 he was a professor at the Collège de France in Paris.

His doctoral students include Winfried Kohnen , Maxim Kontsevich , Nils-Peter Skoruppa , Sander Zwegers , Svetlana Katok and Maryna Viazovska .

Mathematical Achievements

With Benedikt Gross in 1986 he solved Gauß's general class number problem of imaginary quadratic number fields by providing a method that was in principle effective (based on an idea by Dorian Goldfeld (1976) that established a connection with the theory of the L-functions of elliptic curves ), to specify the list of imaginary square class bodies with a certain number of classes. The special case of class number 1 (in which the prime factorization is unambiguous, and which CF Gauss had originally dealt with) had already been proven by Kurt Heegner and Harold Stark . In their work Gross and Zagier also gave a partial solution to the conjecture of Birch and Swinnerton-Dyer (order r of the zero s = 1 of the L-function of an elliptic curve is equal to the rank r of the "additive" group of rational points on the curve) . They proved that the rank of the group of rational points is at least 1 if the order of the zero L (1) is 1.

In addition to the theory of Diophantine equations , which he also researched numerically as a programmer, he was a. a. with modular forms and their periods (many play a role as “ motifs ” in number theory) and with Jacobiforms (he worked there with Martin Eichler and Nils-Peter Skoruppa ). Recently he has been working on theta functions on indefinite square shapes.

He proved the conjecture that the values ​​of Dedekind's zeta function for the natural numbers can be expressed by polylogarithms . In addition, it created a connection to hyperbolic manifolds (rooms negative curvature), where even Lobachevski the volume of a three-dimensional simplex by Dilogarithmen expressed. He also worked on the relationship between knot invariants and multiple zeta functions .

With Harer he proved a conjecture about the Euler characteristic of the modular spaces of Riemann surfaces by gender , which is then equal to the value of the Riemann zeta function at . He also studied the combinatorics of the cell breakdown of these modular rooms. This work also has applications in string theory (where perturbation theory leads to the consideration of Riemann surfaces of arbitrarily high sex, on which the fundamental particles are defined as gauge fields or spinor fields ).

With Martin Möller , he calculated the Taylor expansion of Teichmüller curves with the help of theta functions . This result thus provided one of the first significant explicit analytical findings on Teichmüller curves.

He also investigated stable rank 2 vector bundles on Riemann surfaces and the associated Verlinde formula (from string theory).

Zagier also works in mathematical physics, e.g. B. in percolation theory .

Awards and memberships

In 1987 he was awarded the Cole Prize and in 2001 the Karl Georg Christian von Staudt Prize . He also received the Carus Medal in 1984 and the Prix ​​Élie Cartan in 1996, as well as the Chauvenet Prize of the AMS in 2000 . In 2004/05 he was on the Abel Prize Committee .

In 1993 he was accepted as a full member of the Academia Europaea . Zagier has been a member of the Leopoldina since 1998 , in 1999 he was elected to the North Rhine-Westphalian Academy of Sciences and Arts , and in 2017 to the National Academy of Sciences .

In 2007 he gave the Gauss lecture at the DMV . In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (L-series and the Green's functions of modular curves) . In 1992 he was invited speaker at the European Congress of Mathematicians in Paris ( Values ​​of zeta functions and their applications ).

Publications (selection)

literature

Web links

Commons : Don Zagier  - collection of images, videos and audio files

Individual evidence

  1. ↑ a b Max Planck Institute for Mathematics Bonn - emeritus scientific members - Don Zagier (accessed on June 13, 2020)
  2. ↑ Möller, Zagier: Modular embeddings of Teichmüller curves, Compositio Mathematica, Volume 152, 2016, pp. 2269-2349, Arxiv
  3. ^ Abel Committee
  4. ^ Membership directory: Don Zagier. Academia Europaea, accessed July 28, 2017 .
personal data
SURNAME Zagier, Don
ALTERNATIVE NAMES Zagier, Don Bernhard
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 29, 1951
PLACE OF BIRTH Heidelberg