Table of Contents

Statements of the main results Reformulation of the main results Reduction steps in proving the main theorems Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromy of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in various families Appendix AD: Densities Appendix AG: Graphs References.