  These notes are an expanded version of a talk given by the second author. Our
main interest is focused on the challenging problem of computing Kronecker
coefficients. We decided, at the beginning, to take a very general approach to
the problem of studying multiplicity functions, and we survey the various
aspects of the theory that comes into play, giving a detailed bibliography to
orient the reader. Nonetheless the main general theorems involving
multiplicities functions (convexity, quasi-polynomial behavior, Jeffrey-Kirwan
residues) are stated without proofs. Then, we present in detail our approach to
the computational problem, giving explicit formulae, and outlining an algorithm
that calculate many interesting examples, some of which appear in the
literature also in connection with Hilbert series.
