

1969  Diploma of Advanced Mathematics, Oxford University, England, UK  1971  D.Phil., Oxford University, England, UK  1971  1984  Scientific Member, DFG Collaborative Research Center SFB 72 “Approximation”, University of Bonn  1975  Habilitation, University of Bonn  1979  1990  Chair Professor of Number Theory, University of Maryland, College Park, MD, USA  1990  2001  Professor, University of Utrecht, Netherlands  1990  1991  Professor, Kyushu University, Fukuoka, Japan  1992  1993  Professor, Kyushu University, Fukuoka, Japan  2000  2014  Professor, Collège de France, Paris, France  Since 1976  APL Professor, University of Bonn  Since 1984  Scientific Member, Max Planck Institute for Mathematics, Bonn  Since 1995  Director, Max Planck Institute for Mathematics, Bonn  Since 2014  Distinguished Staff Associate, International Centre for Theoretical Physics, Trieste, Italy 


Modular forms, which are my main area of research, can be seen as part of both the theory of automorphic forms and of moduli spaces (Research Area DE), but are also of great importance in many parts of quantum field theory and string theory (Area C). My research in the last years has touched all these aspects, two examples being my work with Dabolkar and Murthy on applications of ''mock modular forms'' (as developed by my then student Zwegers, myself and others) to the string theory of black holes and my recent work with Möller on applications of the theory of modular and quasimodular forms to Teichmüller curves and to moduli spaces of flat surfaces. With Garoufalidis I have also been studying the arithmetic of quantum invariants of knots: we proved some cases of the conjectured ''quantum modularity'' properties of Kashaev invariants that I had discoved experimently ten years ago and, in joint work with Frank Calegari, found a construction of algebraic units from classes in algebraic Ktheory having as an unexpected consequence a proof of Nahm's conjecture relating modularity to algebraic Ktheory.
Recently I have become interested in the arithmetic and topology of differential equations (the subject of the ''Hirzebruch Lecture'' that I gave at the ECM 2016). Together with Vasily Golyshev, with whom I have already published one paper on the subject (proving the socalled ''Gamma Conjecture'' for all rank one Fano 3folds) and others (in particular Masha Vlasenko and Spencer Bloch), I am studying the relation of ''motivic gamma functions'' (a kind of Mellin transform of solutions of PicardFuchs differential equations) and Hirzebruchlike characteristic classes of algebraic varieties. In other directions, I am studying together with Lin Weng the properties of the ''higher rank zeta functions'' of curves over finite fields that he defined some years ago (in particular, we proved the Riemann hypothesis for the genus one case and are working on the general case), and am also working with T. Ibukiyama to extend our theory of ''higher spherical polynomials'' to a theory of higher spherical functions. Finally, in collaboration with Martin Möller and others (recently Di Yang and Boris Dubrovin), we are extending our earlier work on combinatorial aspects of moduli spaces (Hurwitz numbers, graph counting, generalizations of the BlochOkounkov theorem, ...).


[ 1] F. Hirzebruch, D. Zagier
Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus Invent. Math. , 36: : 57113 1976 DOI: 10.1007/BF01390005[ 2] Martin Eichler, Don Zagier
The theory of Jacobi forms of Progress in Mathematics : v+148 Publisher: BirkhÃ¤user Boston, Inc., Boston, MA 1985 ISBN: 0817631801 DOI: 10.1007/9781468491623[ 3] Benedict H. Gross, Don B. Zagier
Heegner points and derivatives of Lseries Invent. Math. , 84: (2): 225320 1986 DOI: 10.1007/BF01388809[ 4] J. Harer, D. Zagier
The Euler characteristic of the moduli space of curves Invent. Math. , 85: (3): 457485 1986 DOI: 10.1007/BF01390325[ 5] J. Lewis, D. Zagier
Period functions for Maass wave forms. I Ann. of Math. (2) , 153: (1): 191258 2001 DOI: 10.2307/2661374[ 6] Don Zagier
Ramanujan's mock theta functions and their applications (after Zwegers and OnoBringmann) SÃ©minaire Bourbaki. Vol. 2007/2008 AstÃ©risque (326): Exp. No. 986, viiviii, 143164 (2010) 2009 ISBN: 9782856292693[7] D. Zagier
Evaluation of the multiple zeta values Î¶(2,ldots,2,3,2,ldots,2) Ann. of Math. (2) , 175: (2): 9771000 2012 DOI: 10.4007/annals.2012.175.2.11 [ 8] Dawei Chen, Martin Moeller, Don Zagier
Quasimodularity and large genus limits of SiegelVeech constants eprint arXiv:1606.04065 : 107 pages 2016[9] V. V. Golyshev, D. Zagir
Proof of the gamma conjecture for Fano 3folds with a Picard lattice of rank one Izv. Ross. Akad. Nauk Ser. Mat. , 80: (1): 2754 2016 DOI: 10.4213/im8343 [ 10] Atish Dabholkar, Sameer Murthy, Don Zagier
Quantum Black Holes, Wall Crossing, and Mock Modular Forms eprint arXiv:1208.4074, to appear in Cambridge Monographs in Mathematical Physics : 151 pages 2012




• Journal of Number Theory (since 1981)
• Selecta Mathematica (since 1994)
• The Ramanujan Journal (since 1994)
• Kyushu Journal (since 1998)
• Ergebnisse der Mathematik und ihrer Grenzgebiete (since 1998)


1984  Carus Prize, Schweinfurt  1987  Frank Nelson Cole Prize in Number Theory  1996  Prix Elie Cartan, Académie des Sciences  2000  Chauvenet Prize of the Mathematical Association of America  2001  Karl Georg Christian von Staudt Prize  2017  Member of the U.S. National Academy of Sciences (NAS) 


Georgia Triantafillou (1977): “Equivariant rational homotopy theory”,
now Professor, Temple University, PA, USA
Winfried Kohnen (1980): “Modular forms of alfintegral weight”,
now Professor, University of Heidelberg
Robert Sczech (1982): “Summation of Lseries”,
now Associate Professor, Rutgers University, NJ, USA
Svetlana Katok (1983): “Modular forms and closed geodesics”,
now Professor, Pennsylvania State University, PA, USA
NilsPeter Skoruppa (1984): “Jacobi and modular forms of halfintegral weight”,
now Professor, University of Siegen
Maxim Kontsevich (1991): “KdV hierarchy and moduli spaces”,
now Permanent Professor, Institut des Hautes Études Scientifiques (IHÉS), France
Herbert Gangl (1994): “Functional equations of polylogarithms”,
now 1H Course Director, Reader, Durham University, England, UK
Sander Zwegers (2002): “Mock theta functions”,
now Professor (tenure), University of Cologne
Anton Mellit (2008): “Higher Green's functions for modular forms”,
now Postdoc, International School for Advanced Studies (SISSA), and Consultant, International Centre for Theoretical Physics (ICTP), Italy
Maryna Viazovska (2013): “Modular Functions and Special Cycles”,
now Postdoc, Berlin Mathematical School, HU Berlin
Danylo Radchenko (2016): “Higher crossratios and geometric functional equations for polylogarithm”,
now Postdoctoral Fellow, International Centre for Theoretical Physics (ICTP), Trieste, Italy
Federico Zerbini (2017): “Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes”,
now at Institut de Physique Théorique, CEA Saclay, France


 PhD theses: 23, currently 2


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