Let Î“ be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if Î“ has the congruence subgroup property, then the number of n-dimensional irreducibleâ€¦ (More)

We generalize two theorems about K-automorphisms from Z to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union ofâ€¦ (More)

We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P.â€¦ (More)

Extending results of [Kaz86] to the relative case, we relate harmonic analysis over some spherical spaces G(F )/H(F ), where F is a field of positive characteristic, to harmonic analysis over theâ€¦ (More)

The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are theâ€¦ (More)

Generalizing Kriegerâ€™s finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra,â€¦ (More)

We study new asymptotic invariant of a pair consisting of a group and a subgroup, which we call Commensurizer growth. We compute the com-mensurizer growth for several examples, concentrating mainlyâ€¦ (More)

Suppose that M is a smooth manifold and Tt : M â†’ M is a flow, i.e. a one-parameter group of diffeomorphisms. One way of studying this flow is by looking at a cross-sectionâ€”that is to say, aâ€¦ (More)