Homogeneous Dynamics and
Applications

This is the third volume of a project that began with the volume Ergodic Theory with a view toward Number Theory by Einsiedler and Ward and continued with Entropy in Ergodic Theory and Topological Dynamics by Einsiedler, Lindenstrauss and Ward. This third volume aims to develop the relationship between the ergodic theory of homogeneous spaces and applications in number theory.

This web page contains some early drafts of some of the planned chapters.

Please send any comments to the authors (if possible mentioning the date of the file you are using), manfred.einsiedler@math.ethz.ch or tbward@gmail.com.

All material on this web page is © M.E. & T.W. 2008-2018.

• Introduction (August 2018)

• Chapter 1: Lattices and the space of lattices (August 2018)

• Chapter 2: Ergodicity and mixing on locally homogeneous spaces (August 2018)

• Chapter 3: Rationality (August 2018)

• Chapter 4: Quantitative non-divergence (September 2018)

• Chapter 5: Action of horospherical subgroups (September 2018)

• Chapter 6: Ratner's theorem in unipotent dynamics (July 2019)

• References (August 2018)