Sebastian Herrero: Special values of Green's functions on hyperbolic 3-space

In 1986, Gross and Zagier proposed a conjecture on the algebraicity of special values of higher Green's functions on modular curves, which mirrors the properties of the modular j-function in the classical theory of complex multiplication. This conjecture was recently proven by Bruinier, Li, and Yang. In this talk, I will present new results on an analogous problem for special values of Green's functions on hyperbolic 3-space. We show that certain finite sums of these special values can be expressed in terms of logarithms of primes and logarithms of units in real quadratic fields. This is joint work with Özlem Imamoglu, Anna von Pippich, and Markus Schwagenscheidt.