# Dynamics, Geometry, Number Theory

## The Impact of Margulis on Modern Mathematics

# Dynamics, Geometry, Number Theory

## The Impact of Margulis on Modern Mathematics

**This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon.**

This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani.

*Dynamics, Geometry, Number Theory*introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research.

*Dynamics, Geometry, Number Theory*provides one remedy to that challenge.

## Reviews

## Table of Contents

Introduction*David Fisher***PART I || ***Arithmeticity, superrigidity, normal subgroups***1. **Superrigidity, arithmeticity, normal subgroups: results, ramifications, and directions *David Fisher***2. **An extension of Margulis’s superrigidity theorem*Uri Bader and Alex Furman***3. **The normal subgroup theorem through measure rigidity*Aaron Brown, Federico Rodriguez Hertz, and Zhiren Wang***PART II || ***Discrete subgroups***4. **Proper actions of discrete subgroups of affine transformations*Jeffrey Danciger, Todd A. Drumm, William M. Goldman, **and Ilia Smilga***5. **Maximal subgroups of countable groups: a survey*Tsachik Gelander, Yair Glasner, and Gregory Soifer***PART III || ***Expanders, representations, spectral theory***6. **Tempered homogeneous spaces II*Yves Benoist and Toshiyuki Kobayashi***7. **Expansion in simple groups*Emmanuel Breuillard and Alexander Lubotzky***8. **Elements of a metric spectral theory*Anders Karlsson***PART IV || ***Homogeneous dynamics***9. **Quantitative nondivergence and Diophantine approximation on manifolds *Victor Beresnevich and Dmitry Kleinbock***10. **Margulis functions and their applications*Alex Eskin and Shahar Mozes***11. **Recent progress on rigidity properties of higher rank diagonalizable actions and applications*Elon Lindenstrauss***12. **Effective arguments in unipotent dynamics*Manfred Einsiedler and Amir Mohammadi***13. **Effective equidistribution of closed hyperbolic subspaces in congruence quotients of hyperbolic spaces*Manfred Einsiedler and Philipp Wirth***14. **Dynamics for discrete subgroups of SL2(C)*Hee Oh*

## Be the first to know

Get the latest updates on new releases, special offers, and media highlights when you subscribe to our email lists!