Don Zagier is a pure mathematician of broad interests, but working primarily in the domain of number theory and the theory of modular forms and their applications in other areas ranging from knot theory to mathematical physics. He has led a rather international life, having been born (in June 1951) of naturalized American parents, spent his first thirteen years in Germany, Japan (in both cases during the American occupation) and six American states and his later years in the United States, six European countries, and Japan. He had an accelerated education, obtaining his high school degree at 13, two bachelor degrees from MIT at 16, and his Ph.D. from Oxford at 20. His mathematical base since his doctorate has been in Germany (where he has been a scientific member of the Max Planck Institute for Mathematics in Bonn since its founding in 1984 and one of its directors since 1995), but he has also always held a position in another country: at the University of Maryland from 1978 to 1990, at the University of Utrecht from 1990 to 2001, at the College de France in Paris from 2001 to 2014, and at the International Centre for Theoretical Physics in Trieste since 2014. His main hobbies are piano and languages.

Research Interests

Don Zagier is above all interested in the interactions between number theory, especially the theory of modular forms, and other fields of mathematics and mathematical physics. Examples are the applications of his work on Heegner points with Dick Gross to the Gauss Class Number Problem and the Birch - Swinnerton-Dyer Conjecture, the many applications in both mathematics and mathematical physics of the theory of Jacobi forms that he developed with Martin Eichler, or the applications (in joint work with two physicists) of the theory of mock modular forms - a discovery of his doctoral student Sander Zwegers - to the string theory of black holes. In recent years he has been especially interested in parts of mathematics coming from quantum field theory and in particular quantum invariants of knots, which turned out also to have a surprising hidden modular behavior.

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Section 11: Mathematics