Seminar: Alex Lubotzky (Weizmann and Fields Institutes) | Department of Mathematics

5:00–6:00 pm Eckhart Hall 206

Uniform Stability of Lattices in High-Rank Semisimple Groups

Abstract:

Lattices in high-rank semisimple groups enjoy a number of special properties like super-rigidity, quasi-isometric rigidity, first-order rigidity, and more. In this talk, we will add another one: uniform ( a.k.a. Ulam) stability. Namely, it will be shown that (most) such lattices D satisfy: every finite-dimensional unitary "almost-representation" of D ( almost w.r.t. to a sub-multiplicative norm on the complex matrices) is a small deformation of a true unitary representation. This extends a result of Kazhdan (1982) for amenable groups and or Burger-Ozawa-Thom (2013) for SL(n,Z), n>2. The main technical tool is a new cohomology theory ("asymptotic cohomology") that is related to bounded cohomology in a similar way to the connection of the last one with ordinary cohomology. The vanishing of H^2 w.r.t. to a suitable module implies the above stability. The talk is based on ongoing work with L. Glebsky, N. Monod, and B. Rangarajan.

Event Type

Nov 28