Event Detail

Event Type: 
Geometry-Topology Seminar
Monday, January 28, 2019 - 12:00 to 12:50
Kidd 237

Speaker Info

University of Washington

In this talk, we will construct an example of a closed Riemann surface $X$ that can be realized as a quotient of a triply periodic polyhedral surface $\Pi \subset \mathbb{R}^3$ where the Weierstrass points of $X$ coincide with the vertices of $\Pi.$ First we construct $\Pi$ by attaching regular octahedra in a periodic manner then consider the surface of this solid. Due to periodicity we can find a compact quotient of this surface. The symmetries of $X$ allow us to construct hyperbolic structures and various translation structures on $X$ that are compatible with its conformal type. The translation structures are the geometric representations of the holomorphic 1-forms of $X.$ Via the basis of 1-forms we find an explicit algebraic description of the surface that suggests that it is Fermat's quartic.