# Program

Homogeneous dynamics is the study of asymptotic properties of the action of subgroups of Lie groups on their homogeneous spaces. This includes many classical examples of dynamical systems, such as linear Anosov diffeomorphisms of tori and geodesic flows on negatively curved manifolds. This topic is related to many branches of mathematics, in particular, number theory and geometry. Some directions to be explored in this program include: measure rigidity of multidimensional diagonal groups; effectivization, sparse equidistribution and sieving; random walks, stationary measures and stiff actions; ergodic theory of thin groups; measure classification in positive characteristic. It is a companion program to “Dynamics on moduli spaces of geometric structures”.
Bibliography (PDF)

**Keywords and Mathematics Subject Classification (MSC)**

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

January 29, 2015 - January 30, 2015 | Connections for Women: Geometric and Arithmetic Aspects of Homogeneous Dynamics |

February 02, 2015 - February 06, 2015 | Introductory Workshop: Geometric and Arithmetic Aspects of Homogeneous Dynamics |

May 11, 2015 - May 15, 2015 | Advances in Homogeneous Dynamics |