Homework Assignment 3

Recall that the upper half plane \mathbb H^2 consists of complex numbers z = x + i \, y with y > 0. Let \overline{\mathbb D} = \left \{ x + i \, y \in \mathbb C \, \bigl| \, x^2 + y^2 \leq 1 \right \} = \mathbb D \cup \partial \mathbb D denote the closed unit disk as the union of the unit disk \mathbb D with its boundary \partial \mathbb D = \left \{ x + i \, y \in \mathbb C \, \bigl| \, x^2 + y^2 = 1 \right \} \simeq S^1(\mathbb R). This assignment is meant to explain the pictures at the Wolfram Demonstrations site as well as on Wikipedia:

This assignment is due Friday, October 18, 2013 at the start of class.

Homework Assignment 3 Download

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“Separated Belyĭ Maps” by Zachary Scherr and Michael E. Zieve

Zachary Scherr and his graduate advisor Michael E. Zieve have a new paper on the ArXiv entitled “Separated Belyĭ Maps”.

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Lecture 15: Monday, September 23, 2013

Today we discuss how some familiar objects — namely the circle, the sphere, the torus, and even elliptic curves — are each examples of non-singular algebraic curves which are also compact, connected Riemann surfaces.

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Lecture 14: Friday, September 20, 2013

Eventually, we wish to show that every compact, connected Riemann surface X is a nonsingular algebraic curve. Today, we discuss what is means to be a “nonsingular algebraic curve” using Dedekind Domains.

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“An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group” by Pierre Guillot

Pierre Guillot has a new paper on the ArXiv entitled “An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group”.

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“Hecke Groups, Dessins d’Enfants and the Archimedean Solids” by Yang-Hui He and James Read

Yang-Hui He and James Read have a new paper on the ArXiv entitled “Hecke Groups, Dessins d’Enfants and the Archimedean Solids”.

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“Regular Dessins with a Given Automorphism Group” by Gareth A. Jones

Gareth A. Jones has a new paper on the ArXiv entitled “Regular Dessins with a Given Automorphism Group”.

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