Lior Silberman

I will give a (necessarily woefully incomplete) introduction to the measure classification paradigm in homogenous dynamics, and discuss one source of invariant measures and application of this paradigm: the Quantum Unique Ergodicity problem.

Let M=SL2(ℤ[i])∖ℍ(3) be the Bianchi orbifold, and let {fn}∞n=1⊂L2(M) be a sequence of Hecke--Maass forms on it. We should that the probability measures on M with densities |fn(x)|2 with respect to the Riemannian volume become equidistributed on M...

I will describe work with Dubi Kelmer on the first Laplace eigenvalue in towers of manifolds covered by real or complex hyperbolic space. All congruence quotients in a given dimension have a uniform spectral gap; we show how to deduce from this a...

Consider the variety \Hom(\Gamma,G) where \Gamma is a finitely generated nilpotent group, and G a semisimple Lie group. I will discuss joint work with Juan Souto on homotopy retractions from this variety to the representation variety in K, a maximal...

Lior speaks on the construction of the apartment for a quasisplit group, as in I.1 of Landvogt.

TBA