Associated to global fields are genuine high rank zeta functions, exposing
non-abelian aspects of the fields. Defined using natural counts over
moduli spaces of stable bundles/lattices, these zetas are canonical as well. For
example, when rank becomes one, they coincide with classical Artin/Dedekind zeta
functions for function fields/number fields. We will talk about their constructions,
basic properties, and related open problems in arithmetic geometry and number theory