Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, November 28, 2016 - 12:00 to 12:45

Location:

Gilkey 115

Institution:

Graduate Student

Abstract:

Compact Riemann surfaces which admit a ramified covering of the Riemann sphere with at most three branching values are in one-to-one correspondence with projective algebraic curves with coefficients in some number field due to Belyi's Theorem from 1979. These coverings are called Belyi functions, and they induce unramified coverings of the thrice punctured sphere. In turn, we have inclusions in fundamental groups. We discuss some examples of this phenomenon. In particular, we observe how a covering of the figure-eight space can be encoded in a dessin (i.e., a bipartite combinatorial graph), and hence also a unique Belyi function and algebraic curve.