This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.
This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.
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.
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.
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