Recommended reading materials

The Clay summer proceedings survey contains a superset of the course (a short discussion of the above prerequisites as well as some more material that we will not cover), see the pdf in

 

(2) For  Alex Eskin's lectures:
Something close to his lecture notes is here: http://math.uchicago.edu/~eskin/luminy2012/lectures.pdf

 

These notes are probably a bit too advanced. One place one can get a general introduction to the subject is this survey paper:

 http://arxiv.org/pdf/math/0609392.pdf

 

 

 

 

 

(3) For Kleinbock's lectures:
here: Kleinbock's lectures

 

 

 

 

(4) For Mohammadi's lectures:
 M. Einsiedler, Ratner’s theorem on SL(2, R)-invariant measures, Jahresber. Deutsch. Math.- Verein. 108 (2006), no. 3, 143–164.

 

 

 

 

 

(5) For Emmanuel Breulliard's lectures:

1) Fell topology, Property (T), and spectral gaps.
2) Expander graphs and approximate groups.
3) Super-strong approximation.

* Here are some references and reading material for the first lecture.

- books:
Kirillov, Elements of the theory of Representations
Zimmer, Ergodic Theory and Semisimple groups
Bekka-de la Harpe-Valette, Kazhdan's property (T).

- papers:
Fell, Weak containment and induced representations of groups.
Moore, Exponential decay of correlation coefficients for geodesic flows.

Cowling, Sur les coefficients des representations unitaires des groupes de Lie simples (in French!).

 

 

*Here is some additional material for second lecture:

 -papers:
 Einsiedler-Margulis-Venkatesh, Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces.
 Furman-Shalom, Sharp ergodic theorems for group actions and strong ergodicity.
 Shalom, Explicit Kazhdan constants for representation of semisimple groups.

 -notes:
 Bump, Spectral theory and trace formula.

 -books:
 Margulis, Discrete subgroups of semisimple groups (Chapter III).
 Sarnak, Applications of modular forms (Chapter 2).


 

*And for my third lecture:

 -papers:
 Bourgain-Gamburd, Uniform expansion bounds for Cayley graphs of SL(2,F_p).
 Breuillard-Green-Tao, Linear approximate groups.
 Pyber-Szabo, Growth in finite simple groups of Lie type.
 Salehi-Golsefidy-Varju, Expansion in perfect groups.

 -notes:
 PCMI notes: http://www.math.u-psud.fr/~breuilla/BreuillardPCMI.pdf
 MSRI notes: http://www.math.u-psud.fr/~breuilla/Breuillard_MSRI.pdf