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MATHEMATICAL WORK

Some of his striking discoveries are:

•His finding with Hirzebruch about intersection numbers of curves on Hilbert modular surfaces being the coefficients of a modular form.

>(with F. Hirzebruch) Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus

My impression is that this marked the birth of the rich theory of special cycles on Shimura varieties.

•His conjecture on expressing special values of Dedekind Zeta functions in terms of polylogarithms.

>Polylogarithms, Dedekind zeta functions, and the algebraic K-theory of fields in Arithmetic Algebraic Geometry (G. v.d. Geer, F. Oort, J. Steenbrink, eds.), Prog. in Math. 89, Birkhäuser, Boston (1990) 391-430 (pdf)

•His work with Benedict Gross giving a formula for norms of differences of singular moduli

>(with B. Gross) Singular moduli J. reine Angew. Math. 355 (1985) 191-220 (pdf)

and his later work showing that traces of singular moduli are the coefficients of a modular form

>Traces of singular moduli In “Motives, Polylogarithms and Hodge Theory (Eds. F. Bogomolov, L. Katzarkov), Lecture Series 3, International Press, Somerville (2002), 209-244 (pdf)

•The Gross-Zagier formula

>(with B. Gross) Heegner points and derivative of L-series
Invent. Math. 85 (1986) 225-320 (pdf)

•The computation of the (orbifold) Euler characteristic of the moduli space of curves of genus g with n marked points

>(with J. Harer) The Euler characteristic of the moduli space of curves
Invent. Math. 85 (1986) 457-485 (pdf)

EXPOSITORY WORK

I’ve found his papers to be a great pleasure to read.

For those who have a solid undergraduate background (including complex analysis), I would strongly recommend his notes on Elliptic Modular Forms and Their Applications (http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/978-3-540-74119-0_1/fulltext.pdf).