Thin Groups and Superstrong Approximation

Emmanuel Breuillard is a Professor at the Laboratoire de Mathématiques, Université Paris-Sud Orsay. He was recently awarded an EMS Prize by the European Mathematical Society for his work in group theory. Hee Oh is a Professor of Mathematics at Brown University. She is an inaugural Fellow of the American Mathematical Society and has given a joint AMS-MAA invited address at the 2012 Joint Mathematics meetings and an invited lecture at the International Congress of Mathematicians in 2010.

1. Some Diophantine applications of the theory of group expansion Jean Bourgain; 2. A brief introduction to approximate groups Emmanuel Breuillard; 3. Superstrong approximation for monodromy groups Jordan S. Ellenberg; 4. The ubiquity of thin groups Elena Fuchs; 5. The orbital circle method Alex V. Kontorovich; 6. Sieve in discrete groups, especially sparse Emmanuel Kowalski; 7. How random are word maps? Michael Larsen; 8. Constructing thin groups Darren Long and Alan W. Reid; 9. On ergodic properties of the Burger-Roblin measure Amir Mohammadi; 10. Harmonic analysis, ergodic theory and counting for thin groups Hee Oh; 11. Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces Gopal Prasad and Andrei Rapinchuk; 12. Growth in linear groups László Pyber and Endre Szabó; 13. On strong approximation for algebraic groups Andrei Rapinchuk; 14. Generic phenomena in groups: some answers and many questions Igor Rivin; 15. Affine sieve and expanders Alireza Salehi Golsefidy; 16. Growth in linear groups Peter Sarnak.