Gauged Gromov-Witten theory and affine grassmannians

Many objects of interest in algebraic geometry (such as curves, vector bundles, or differential equations) are parametrized by algebraic varieties, called moduli spaces. 
In this talk I will discuss some recent techniques developed to construct moduli spaces for the moduli of decorated principal bundles on a fixed compact Riemann surface.
With time permitting, I will also explain what it means to count vector bundles on compact Riemann surfaces, and why such counts are given by combinations of certain special values of transcendental functions. 
This talk is based on joint work with Daniel Halpern-Leistner.