Monthly Archives: September 2013

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. Advertisements

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Lecture 14: Friday, September 20, 2013

Eventually, we wish to show that every compact, connected Riemann surface 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-Teichm├╝ller 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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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

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Lecture 12: Monday, September 16, 2013

Last time, we introduced the Fundamental Domain in terms of the extended complex plane . Felix Klein showed the existence of a function , invariant under , giving these isomorphisms. Today, we use Richard Dedekind‘s function to create similar functions … Continue reading

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