Monthly Archives: September 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
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.
“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”.
Yang-Hui He and James Read have a new paper on the ArXiv entitled “Hecke Groups, Dessins d’Enfants and the Archimedean Solids”.
Gareth A. Jones has a new paper on the ArXiv entitled “Regular Dessins with a Given Automorphism Group”.
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
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