M. Kisin - Hilbert's thirteenth problem and the moduli space of abelian varieties

The (multi-valued) solution of a general polynomial of degree n is a priori a function of n-1 variables. Hilbert's thirteenth problem and its variants ask when such functions can be written as a composite of functions in a smaller number of variables. I will explain some progress on this question which uses the geometry of A_g.
This is joint work with Benson Farb and Jesse Wolfson.