## The space of surface shapes, and some applications to biology

Joel Hass

University of California, Davis; Member, School of Mathematics

February 1, 2016

The problem of comparing the shapes of different surfaces turns up in different guises in numerous fields. I will discuss a way to put a metric on the space of smooth Riemannian 2-spheres (i.e. shapes) that allows for comparing their geometric similarity. The metric is based on a distortion energy defined on the space of conformal mappings between a pair of spheres. I'll also discuss a related idea based on hyperbolic orbifold metrics. I will present results of experiments on applying these techniques to biological data.