# Geometria em Lisboa Seminar

### Supersymmetric quantum mechanics on vortex moduli spaces.

I will describe joint work with M. Boekstedt and C. Wegner aiming at uncovering fundamental features of $N=(2,2)$ supersymmetric quantum mechanics on moduli spaces of vortices on compact Riemann surfaces, in analogy with the spectrum of quantum dyon-monopole bound states that emerged in connection with Sen's S-duality conjectures in the 1990s. My focus in this talk will be on the (topological A-twisted) supersymmetric Abelian Higgs model coupling to local systems, for both linear and nonlinear targets; the corresponding ground states can be investigated by means of the theory of $L^2$-invariants applied to the natural Kaehler metrics on the moduli spaces. I shall explain why the quanta of such Abelian gauge theories can nontrivially realize non-Abelian statistics in particular examples, and motivate a precise conjecture regarding the nonlinear superposition of ground states.

Current organizer: Rosa Sena Dias