# Tag Archives: Mobius Transformation

## Lecture 13: Wednesday, September 18, 2013

In Lecture 11 and Lecture 12, we discussed examples of Riemann Surfaces and their relation with the Riemann Sphere . Today, we put things into perspective by considering the larger picture: we discuss tesselations of the upper half plane, covering … Continue reading

## Homework Assignment 2

Recall that the collection of Möbius transformations is the group while the (ordinary) triangle group is the set This homework set is meant to discuss the relationship with these two sets. This assignment is due Friday, September 20, 2013 at … Continue reading

## Lecture 7: Wednesday, September 4, 2013

Let denote either , , or . The collection of rational functions which have are called Möbius Transformations. That is, they are in the form where . We denote this collection by . We found in the previous lecture that … Continue reading

## Lecture 6: Friday, August 30, 2013

Groups were first studied as objects acting on sets. For example, we can consider the group of rotations of a regular polygon. Eventually, we wish to consider a specific type of group acting on the collection of rational functions over … Continue reading

## Constructing BelyÄ 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

## Lecture 1: Monday, August 19, 2013

For the first lecture for the course, I would like to focus on a simple question: Why would anyone care about Dessins d’Enfants anyway? I won’t quite get to answer this question, but I will at least motivate the study … Continue reading

## REUF4: Research Experiences for Undergraduate Faculty

During June 4-8, 2012, I lead a research group on the subject at the Research Experiences for Undergraduate Faculty (REUF) at ICERM in Providence, Rhode Island. Here is a summary of the main results we found during the 2012 summer … Continue reading