Algebraic approach to vortex moduli

After a brief introduction to algebraic stacks, I will give an
overview of the algebraic version of the moduli space of vortices:
a stack of gauged maps with target X over C, where X is a projective
variety where a reductive group acts, and C a projective curve
where the vortices live. I will then introduce the notion of Mundet
semi-stability for gauged maps, and define gauged Gromov-Witten
invariants using this construction.