Distinguishing filling curve types via special metrics

The study of extremal lengths of curves and their relations to intersection numbers has a very rich history. In this talk, I look at filling curves on hyperbolic surfaces and consider its length infima in the moduli space of the surface as a type invariant. Then explore the relations between this geometric invariant and a topological namely the self-intersection number of a curve . In particular, for all finite type surface, construct infinite families of filling curves that cannot be distinguished by self-intersection number but via length infimum. Time permitting, I will also discuss some coarse bounds on the metrics associated to these infimum lengths.