Edray Herber Goins

Pomona College

Visualizing Toroidal Belyĭ Pairs

Colloquium

Thursday, February 25, 2021

4 p.m. EST

Online talk using Zoom

Abstract: A Belyĭ map $\beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C)$ is a rational function with at most three critical values; we may assume these values are $\{ 0, \, 1, \, \infty \}$. A Dessin d’Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: $\beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R)$.

Replacing $\mathbb P^1$ with an elliptic curve $E$, there is a similar definition of a Belyĭ map $\beta: E(\mathbb C) \to \mathbb P^1(\mathbb C)$. The corresponding Dessin d’Enfant can be drawn on the torus by composing with an elliptic logarithm: $\beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R)$. In this project, we use the open source $\texttt{Sage}$ to write code which takes an elliptic curve $E$ and a Belyĭ map $\beta$ to return the Dessin d’Enfant of this map -- both in two and three dimensions. We focus on several examples of Belyĭ maps which appear in the $L$-Series and Modular Forms Database (LMFDB).

A Dream Deferred: 50 Years of Blacks in Mathematics

Public lecture

Thursday, February 25, 2021

7 p.m. EST

Online talk using Zoom

Abstract: In 1934, Walter Richard Talbot earned his Ph.D. from the University of Pittsburgh; he was the fourth African American to earn a doctorate in mathematics. Unfortunately, opportunities for African Americans during that time to continue their research were severely limited. “When I entered the college teaching scene, it was 1934,” Talbot is quoted as saying. “It was 35 years later before I had a chance to start existing in the national activities of the mathematical bodies.” Concerned with the exclusion of African Americans at various national meetings, Talbot helped to found the National Association of Mathematicians (NAM), the nationwide organization of African Americans in Mathematics, in 1969. In this talk, we take a tour of the mathematics done by African and African Americans over the past 50 years since the founding of NAM, weaving in personal stories and questions for reflection for the next 50 years.

NB: PDF version of this announcement (suitable for posting).