Dami Lee, UW

PDL C401
Abstract: In this talk, we plan to find geometric realizations of cyclic branched covers over spheres as triply periodic polyhedral surfaces. In the pretalk, we will investigate a specific example and a brief theory of cyclic covers over spheres. In the main talk, we relax CoxeterPetrie’s definition of infinite regular polyhedra to construct such surfaces whose polyhedral metrics induce conformal structures. This classification yields surfaces that are conformally equivalent to wellknown surfaces such as Fermat's quartic, Schoen’s minimal IWP surface, and Kepler’s small stellated dodecahedron.