Vector-valued modular forms and matrix-valued hypergeometric functions

A general theory of vector-valued modular forms is presented. In my talk I'll focus on weakly holomorphic vector-valued modular functions and their relation to a generalised hypergeometric equation, but time permitting I'll also describe the resulting dimension formulas for holomorphic vector-valued modular forms. I'll also demonstrate with examples how this theory is conducive to explicit calculations of Fourier coefficients.