# Mathematics Colloquium

Speaker:
We will describe new work on finding geodesics on Platonic solids connecting vertices (joint with Aulicino and Hooper), via the theory of translation surfaces, which are surfaces obtained by identifying parallel sides of Euclidean polygons by translations. These surfaces are flat at all but a finite set of points where they have cone-type singularities with angles integer multiples of $2\pi$. We will discuss problems of finding and counting saddle connections, geodesic segments connecting singular points. This talk will be elementary, will have lots of pictures, and will assume little background beyond undergraduate complex analysis