Invariant Random Subgroups

Sde-Boker, Israel;

February 26th to March 2nd 2012.


Scientific background

An invariant random subgroup (IRS) of a group G is a conjugation invariant probability distribution on the space of (closed) subgroups of G. This notion has attracted a lot of attention in the past few years as it seems to provide new and useful connections between measurable group theory, probability and combinatorics. In the setting of ergodic theory, such subgroups arises as the stabilizer of a random point, whenever G acts on a probability space. In probability theory, such a subgroup gives rise to a 'unimodular random network of Schreier graphs' - Sch(G/H, S). In combinatorics, such unimodular random networks arise naturally as Benjamini-Schramm limits of sequences of finite regular graphs. This triple connection gives rise to exciting new results and research directions in all three disciplines. IRS-es are also being studied in connection with rigidity, geometry and representation theory and have been used in the theory of Lie groups and arithmetic groups.

Participants (in alphabetical order)

  1. Miklos Abert (Renyi Institute, Budapest)
  2. Meny Akka (Hebrew University)
  3. Gidi Amir (Bar-Ilan)
  4. Nir Avni (Harvard)
  5. Uri Bader (Technion)
  6. Itai Benjamini (Weizmann Institute)
  7. Nicolas Bergeron (Jussieu)
  8. Ian Biringer (Yale)
  9. Lewis Bowen (Texas A&M)
  10. Gabor Elek (Renyi Institute, Budapest)
  11. Hilary Finucane (Weizmann Institute)
  12. Damien Gaboriau (L'ecole Normale Superieure, Paris)
  13. Tsachik Gelander (Hebrew University)
  14. Eli Glasner (Tel-Aviv University)
  15. Yair Glasner (Ben-Gurion University)
  16. Rostislav Grigorchuk (Texas A&M)
  17. Denis Gulko (Ben-Gurion)
  18. Yair Hartman (Weizmann Institute),
  19. Erez Lapid (Hebrew University)
  20. Daniel Kitroser (Ben-Gurion)
  21. Omer Lavi (Technion)
  22. Gabor Lippner (Harvard)
  23. Vadim Kaimanovich (University of Ottawa)
  24. Gady Kozma (Weizmann Institute)
  25. Erez Lapid (Hebrew University)
  26. Nicolas Monod (EPFL)
  27. Shahar Mozes (Hebrew University)
  28. Amos Nevo (Technion),
  29. Nikolay Nikolov (Imperial College),
  30. Izhar Oppenheim (Technion)
  31. Doron Puder (Hebrew University)
  32. Jean Raimbault (Jussieu)
  33. Pascal Roli (ETH Zurich)
  34. Beatrice Pozzetti (ETH Zurich)
  35. Iddo Sammet (University of Illinois at Chicago)
  36. Roman Sauer (Universitat Regensburg)
  37. Zohar Shapira (Technion)
  38. Tatiana Smirnova-Nagnibeda (Geneva)
  39. Amit Solomon (Hebrew University)
  40. Yaar Solomon (Ben-Gurion)
  41. Andreas Thom (Leipzig)
  42. Anatoly Vershik (St. Petersburg)
  43. Balint Virag (Toronto)
  44. Barak Weiss (Ben-Gurion University)
  45. Benjy Weiss (Hebrew University)

* = awaiting approval.


List of minicourses and lectures

  • Nir Avni - Opening lecture,
  • A measurable Kesten theorem - 3 hours given by Abert and Virag.
  • Asymptotics of Betti numbers in arithmetic manifolds - 5 hours given by Bergeron, Biringer, Gelander, Nikolov and Raimbault
  • IRS in linear groups - 2 hours given by Bader and Glasner
  • IRS in the free groups - 2 hours given by Lewis Bowen
  • Gabor Elek - TBA
  • Damien Gaboriau - TBA
  • Eli Glasner - TBA
  • Tatiana Smirnova-Nagnibeda - TBA
  • Adnreas Thom - TBA
  • Anatoly Vershik - TBA
  • Benjy Weiss - TBA

Full program will be published later.

Time Schedule

Lectures will start on Sunday February 26th at 14:00 and end on Friday March 2nd after lunch. A typical day schedule will contain four formal lectures as well as time for informal activities as follows:

Daily schedule

  • 7:30-9:00 Breakfast;
  • 9:00-10:00 Lecture;
  • 10:00-10:30 Coffee;
  • 10:30-11:30 Lecture;
  • 11:50-12:50 Lecture;
  • 13:00-14:00 Lunch;
  • 16:30-17:30 Lecture.
  • 19:00-20:00 Dinner.

On Wednesday February 29th there will be an excursion instead of the afternoon session.


More practical issues

Funding: Full board will be covered for all conference participants. At the moment we do not expect to have enough money to support travel reimbursements. Nevertheless if you wish to come and have a problem funding the flight please do let us know.

The location: Sde-Boker is a desert campus of Ben-Gurion university of the Negev, located in the beautiful vicinity of the Tzin Creak. It is about one hour drive from Be'er Sheva city.

Facilities: There is a small supermarket on campus but not much more than that.

Transportation: Transportation will be arranged to and from Sde-Boker, the exact details depend on the flight schedules of the participants. So if you are coming please send us your itinerary as soon as you have it so that we can guarantee your transportation to Sde-Boker. Public transportation to the Sde-Boker campus is not very good.

Weather: The temperatures in Sde-Boker in February normally range between 5-20 Centigrade and it might occasionally rain.

Funded by

European Research Council (ERC)/grant agreement 203418

The Center for Advanced Studies at Ben Center for Advanced Studies at Ben-Gurion University