Wednesday 07 Jun 2017: Pseudocenters for Fuchsian tessellations
Montserrat Alsina - Universitat Politecnica de Catalunya and University of Bristol
From the hyperbolic uniformization of Shimura curves Fuchsian tessellations can be considered. This leads to infinitely many tessellations, in contrast with the Euclidian case, and they have been used by several authors to design signal constellations and nonuniform Fuchsian codes. Designs are based on the election of a center in the fundamental tile. Construction of the fundamental domain, by using quaternion algebras and quadratic forms, and hyperbolic constellations will be reviewed. Since the performance of the codes depends on the distance between the constellation points and the sides of the hyperbolic polygons, a study of polygon centers is convenient. In this direction we will discuss a new approach to pseudoincenters for hyperbolic polygons.