Heeyeon Kim: Moduli space of vortices and 3d supersymmetric gauge theories

Abstract: I will discuss the geometric interpretation of the twisted index of 3d supersymmetric gauge theories on a closed Riemann surface. I will show that the twisted index reproduces the virtual Euler characteristic of the moduli space of solutions to vortex equations on the Riemann surface. I will also discuss 3d N = 4 mirror symmetry in this context, which implies non-trivial relations between enumerative invariants associated to the moduli space of vortices. Finally, I will comment on level structures and a wall-crossing formula of the twisted indices derived from the gauge theory point of view.