In-Person and Online Talk 

Zoom Link: https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

Let S be a surface of negative Euler characteristic and C a collection of closed curves. The set of tangent lines to C is a link in the projective tangent bundle PT(S) and drilling this link, we obtain a 3-manifold M_C. Any invariant of M_C is automatically a mapping class group invariant of C. Further, M_C uniquely determines this mapping class group orbit. In this talk, we will go over results that explain the behavior and provide coarse bounds on the hyperbolic volume of M_C  in terms of topological and geometric properties of the family C. For example, when C is a filling pair of simple closed curves, we show that the volume is coarsely comparable to Weil-Petersson distance between strata in Teichmuller space. Lastly, we will explain algorithmic methods and tools for building such links and computing other invariants. This work is joint with Tommaso Cremaschi, Jacob Intrater,  and Jose Andres Rodriguez-Migueles.