The workshop will focus on recent developments concerning various quantitative aspects of "thin groups". These are discrete subgroups of semisimple Lie groups which are both « big » (i.e. Zariski dense) and « small » (i.e. of infinite co-volume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading for instance to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap (super-strong approximation). Simultaneously and sometimes surprisingly, the study of thin groups turns out to be of fundamental importance in a variety of subjects, including equidistribution of homogeneous flows and lattice points counting problems, dynamics on Teichmuller space, the Bourgain-Gamburd-Sarnak sieve in orbit, and arithmetic or geometric properties of certain types of monodromy groups and coverings. The workshop will gather a variety of experts from group theory, number theory, ergodic theory and harmonic analysis to present the accomplishments to date to a broad audience and discuss directions for further study. Scheduled Speakers: 2-hour introductory mini-courses by: E. Breuillard J. Ellenberg A. Gamburd E. Kowalski H. Oh 1-hour talks by: J. Bourgain E. Fuchs A. Kontorovich A. Mohammadi C. McMullen G. Prasad L. Pyber A. Rapinchuk I. Rivin A. Salehi-Golsefidy Bibliography (PDF) Notes by Peter Sarnak (PDF) Accommodation: A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. A block of rooms has been reserved at the Hotel Durant. Please mention MSRI and the workshop name when making reservations via phone, fax or e-mail. If you are making your reservations on line, please go to Hotel Durant website, choose your dates of stay and enter the "123MSRI" promo code in the box. The cut-off date for reservations is January 5, 2012. The rate is $110 per night plus tax. MSRI has a preferred rate of $142 at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI rate; or go to Hotel Shattuck Plaza and enter dates of stay at top of screen and click Book Now.  Once on the reservation page, click Preferred/Corporate Rate Accounts and input the code "MSRI11".