Homogeneous Flows, Moduli Spaces and Arithmetic

This book contains a wealth of material concerning two very active and interconnected directions of current research at the interface of dynamics, number theory and geometry. Examples of the dynamics considered are the action of subgroups of SL (n, R) on the space of unit volume lattices in Rn and the action of SL (2, R) or its subgroups on moduli spaces of flat structures with prescribed singularities on a surface of genus ≥ 2.

The text includes comprehensive introductions to the state-of-the-art in these important areas and several surveys of more advanced topics, including complete proofs of many of the fundamental theorems. on the subject. It is intended for graduate students and researchers wishing to study these fields either for their own sake or as tools to be applied in a variety of fields such as arithmetic, Diophantine approximations, billiards, etc.