|Date: Friday, January 12, 2018
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: Curves defined over the algebraic numbers, Belyi's theorem, and les dessins d'enfants.
Abstract: In the study of smooth, projective curves over the complex numbers, a natural arithmetic question arises: which such curves are defined over the algebraic numbers? Said differently, which such curves are cut out by homogeneous polynomials with coefficients in some number field?
A fantastic result of Belyi asserts that there is a purely algebro-geometric criterion for this arithmetic problem and, in addition, it can be rephrased purely in terms of combinatorial objects (known as un dessin d'enfants).
Our goal is to describe the relationship between the arithmetic, algebro-geometric, and combinatorial facets of this problem (largely through examples), and explain some of the ideas behind Belyi's theorem. This talk will be accessible to anyone who has taken 631.
Speaker: Matt Stevenson