# Category Archives: General Remarks

## Monodromy Groups and Compositions of Belyi Maps

A few weeks ago, I considered how the monodromy groups of Shabat polynomials change under composition by considering several examples. I would like to explain a general phenomenon by considering the composition of Belyi maps on the sphere. Say that … Continue reading

## System of Equations for Computing Shabat Polynomials

A few weeks ago, Dong Quan Ngoc Nguyen (University of Notre Dame) came to visit here at Purdue. We spoke a little about the computer package Bertini (created by Daniel Bates, Jonathan Hauenstein, Andrew Sommese and Charles Wampler) and whether the homotopy … Continue reading

## Monodromy Groups and Compositions of Shabat Polynomials

Last week, the great Naiomi Cameron visited me for a few days to discuss some new directions about Shabat polynomials. I’ve been horrible about posting on this blog, so now that I’ve been motivated to work on Shabat polynomials again, … Continue reading

## Constructing Belyĭ Maps from Valencies

Recently Kevin Pilgrim asked how one could construct a Belyĭ Map from a given set of valencies. I’ll cover this idea in more detail in my course, but I thought I’d put out a general answer now for those who … Continue reading

## What is a “Dessin d’Enfant”?

For the past couple of years, I’ve been thinking about properties of Dessins d’Enfants. As my very first post, I’d like to give a rigorous definition. This is meant to be formal for the math folks out there who are … Continue reading