Fourth meeting, Ben Gurion University 7.5.2013, building 58, seminar room -101

Sponsored by the Center for Advanced Studies in Mathematics, Ben Gurion University

Yet another look at group boundaries.

Invariant random subgroups, lattices and rigidity.

The framework of Invariant Random Subgroups generalizes the notion of lattices and yields a compact space in which all lattices live and on which one can do analysis. Studying the structure of this space and the action of the ambiant group on it gives, in turn, new results about lattices. For instance, applying classical rigidity theorems one deduces that higher rank locally symmetric manifolds of large volume are "almost anywhere fat". Various results about the asymptotic of L_2 invariants of lattices, follow from this fact. More precise statements and some explanations will be given in the talk.

Based on a joint work with Abert, Bergeron, Biringer, Nikolov, Raimbault and Samet.

Mostow rigidity theorem from measured equivalence perspective.

In the late 1960's Mostow discovered a remarkable rigidity property of hyperbolic manifolds - they are completely determined by their fundamental group. This discovery resulted in the celebrated Mostow Rigidity Theorem. After surveying this result I will explain its reformulation within the framework of Measure Equivalence of groups. This new formulation motivates the definition of a slightly stronger rigidity property: Measure Equivalence Rigidity. It turns out that the groups considered by Mostow indeed satisfy this stronger property. I will explain this new result and open questions around it.

Based on a joint work with Alex Furman and Roman Sauer.

(jointly with Ben Gurion University math colloquium)

TBA

4-dimensional arithmetic hyperbolic manifolds and quantum error correcting codes.

A family of quantum error correcting codes (QECC) is constructed out of congruence quotients of the 4- dimensional hyperbolic space. Using methods of systolic geometry over Z/2Z, we evaluate the parameters of these codes and disprove a conjecture of Ze'mor who predicted that such homological QECC do not exist. All notions will be defined and explained. A joint work with Larry Guth.

The meeting will take place in the math Department seminar room, building 58, room -101, Ben Gurion University. You are cordially invited.