Dynamics, Geometry, Number Theory

David Fisher is the Ruth N. Halls Distinguished Professor of Mathematics at Indiana University, Bloomington. Dmitry Kleinbock is professor of mathematics at Brandeis University. Gregory Soifer is professor emeritus of mathematics at Bar-Ilan University, Israel.

• IntroductionDavid FisherPART I || Arithmeticity, superrigidity, normal subgroups1. Superrigidity, arithmeticity, normal subgroups: results, ramifications, and directions David Fisher2. An extension of Margulis’s superrigidity theoremUri Bader and Alex Furman3. The normal subgroup theorem through measure rigidityAaron Brown, Federico Rodriguez Hertz, and Zhiren WangPART II || Discrete subgroups4. Proper actions of discrete subgroups of affine transformationsJeffrey Danciger, Todd A. Drumm, William M. Goldman, and Ilia Smilga5. Maximal subgroups of countable groups: a surveyTsachik Gelander, Yair Glasner, and Gregory SoiferPART III || Expanders, representations, spectral theory6. Tempered homogeneous spaces IIYves Benoist and Toshiyuki Kobayashi7. Expansion in simple groupsEmmanuel Breuillard and Alexander Lubotzky8. Elements of a metric spectral theoryAnders KarlssonPART IV || Homogeneous dynamics9. Quantitative nondivergence and Diophantine approximation on manifolds Victor Beresnevich and Dmitry Kleinbock10. Margulis functions and their applicationsAlex Eskin and Shahar Mozes11. Recent progress on rigidity properties of higher rank diagonalizable actions and applicationsElon Lindenstrauss12. Effective arguments in unipotent dynamicsManfred Einsiedler and Amir Mohammadi13. Effective equidistribution of closed hyperbolic subspaces in congruence quotients of hyperbolic spacesManfred Einsiedler and Philipp Wirth14. Dynamics for discrete subgroups of SL2(C)Hee Oh

"Margulis is without a doubt one of the most influential mathematicians of the past fifty years. The book Dynamics, Geometry, Number Theory is vast in scope and provides an excellent introduction to Margulis's work and the research that it has inspired. It will be of great interest not only to specialists, but to graduate students and researchers interested in ergodic theory, Lie theory, geometry, and number theory."