MCS Seminar: Tan Ser Peow. Hyperbolic jigsaws and families of pseudomodular surfaces

6 September 2017 (Wed), 14:30-15:20
At Classroom 17

Abstract: A pseudomodular group is a Fuchsian group which is not commensurable with the modular group PSL(2,Z) but which has cusp set all of the rationals, the corresponding surface is called a pseudomodular surface. We show that there are infinitely many commensurability classes of pseudomodular groups/surfaces, thus answering a question raised by Long and Reid. We do this by introducing a general construction of surfaces whose fundamental domains are obtained by gluing together marked ideal triangular tiles, which we call hyperbolic jigsaw surfaces. This is joint work with Beicheng Lou and Anh Duc Vo.