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Workshop

Hot Topics: Thin Groups and Super-strong Approximation February 06, 2012 - February 10, 2012
Registration Deadline: February 06, 2012 almost 3 years ago
To apply for Funding you must register by: November 06, 2011 about 3 years ago
Series: Hot Topic
Location:
Organizers Emmanuel Breuillard* (Universite Paris-Sud, Orsay), Alexander Gamburd (CUNY Graduate Center), Jordan Ellenberg (University of Wisconsin - Madison), Emmanuel Kowalski (ETH Zurich), Hee Oh (Brown University)
Speaker(s)

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Description

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".


Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. 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 the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax 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- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
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Feb 06, 2012
Monday
09:00 AM - 09:45 AM
  Welcome and Registration
09:45 AM - 10:00 AM
  Introduction by the MSRI director and staff
10:00 AM - 11:00 AM
  Mini-course 1: Expander Graphs, Thin Groups, and Super-strong Approximation
Alexander Gamburd (University of California, Santa Cruz)
11:00 AM - 11:30 AM
  Tea
11:30 AM - 12:30 PM
  On Zaremba\'s conjecture
Jean Bourgain (Institute for Advanced Study)
12:30 PM - 02:10 PM
  Lunch
02:10 PM - 03:10 PM
  Mini-course 2: Effective circle count for Apollonian circle packings, via spectral methods
Hee Oh (Yale University)
03:10 PM - 03:40 PM
  Tea
03:40 PM - 04:40 PM
  On the Strong Density Conjecture for Apollonian Circle Packings
Alex Kontorovich
Feb 07, 2012
Tuesday
09:00 AM - 10:00 AM
  Mini-course 1: Expander Graphs, Thin Groups, and Super-strong Approximation
Alexander Gamburd (University of California, Santa Cruz)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  On the strong approximation in algebraic groups
Andrei Rapinchuk
11:35 AM - 12:35 PM
  Mini-course 3: Sieve in discrete groups, Part I
Emmanuel Kowalski (Eidgenössische TH Zürich-Hönggerberg)
12:35 PM - 02:10 PM
  Lunch
02:10 PM - 03:10 PM
  Mini-course 2: Counting for orbits of thin groups, via ergodic methods
Hee Oh (Yale University)
03:10 PM - 03:40 PM
  Tea
03:40 PM - 04:40 PM
  Mini-course 4: Approximate groups, Part I
Emmanuel Breuillard (Université Paris-Sud (Orsay))
04:40 PM - 06:15 PM
  Reception
Feb 08, 2012
Wednesday
09:00 AM - 10:00 AM
  Mini-course 5: Thin groups as monodromy groups, Part I
Jordan Ellenberg (University of Wisconsin)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Affine sieve and expanders
Alireza Salehi Golsefidy (University of California, San Diego)
11:35 AM - 12:35 PM
  Dynamics of units and packing constants of ideals
Curtis McMullen (Harvard University)
Feb 09, 2012
Thursday
09:00 AM - 10:00 AM
  Mini-course 3: Sieve in discrete groups, Part II
Emmanuel Kowalski (Eidgenössische TH Zürich-Hönggerberg)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  3-Manifold groups, surface groups and thin subgroups of SL(3,Z)
Alan Reid (University of Texas)
11:35 AM - 12:35 PM
  Mini-course 5: Thin groups as monodromy groups, Part II
Jordan Ellenberg (University of Wisconsin)
12:35 PM - 02:10 PM
  Lunch
02:10 PM - 03:10 PM
  Growth in linear groups
Laci Pyber
03:10 PM - 03:40 PM
  Tea
03:40 PM - 04:40 PM
  Informal and Optional Problem Session
Feb 10, 2012
Friday
09:00 AM - 10:00 AM
  How generic are thin groups?
Elena Fuchs (University of Illinois at Urbana-Champaign)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Mini-course 4: Approximate groups, Part II
Emmanuel Breuillard (Université Paris-Sud (Orsay))
11:35 AM - 12:35 PM
  Weakly-commensurable Zariski-dense subgroups and isospectral arithmetic compact locally symmetric spaces
Gopal Prasad
12:35 PM - 02:10 PM
  Lunch
02:10 PM - 03:10 PM
  Asymptotic properties of obscure groups
Igor Rivin
03:10 PM - 03:40 PM
  Tea