Stephen Kudla "Generating series in arithmetic geometry and modular forms"

Stephen Kudla (University of Toronto)
Generating series in arithmetic geometry and modular forms

The most basic examples of modular generating series are the classical theta series, whose Fourier coefficients are given by the representation numbers of positive definite quadratic forms. In this lecture, I will discuss the problem of constructing analogous series from special arithmetic cycles on certain moduli spaces for abelian varieties. I will focus on the most basic example of arithmetic 0-cycles on the moduli space of CM elliptic curves and explain the relation to the derivatives of incoherent Eisenstein series -- the arithmetic Siegel-Weil formula. As time permits, I will survey some more general examples and speculations.