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Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, January 28, 2019 - 12:00 to 12:50

Location:

Kidd 237

Guest Speaker:

Institution:

University of Washington

Abstract:

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.