The Bernoulli convolution with parameter $\lambda\in (0, 1) $ is the measure on $\bf R $ that
is the distribution of the random power series $\sum\pm\lambda^ n $, where $\pm $ are …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to
have the unique trace property if its reduced C*-algebra has a unique tracial state. A …

We establish various results on the structure of approximate subgroups in linear groups
such as SL n (k) that were previously announced by the authors. For example, generalising …

This paper is concerned with the following general problem. We are given a group G
generated by a finite set S. Suppose that G contains elements with a certain property P. Can …

Let μ μ be a measure on SL _ 2 (R) SL 2 (R) generating a non-compact and totally
irreducible subgroup, and let ν ν be the associated stationary (Furstenberg) measure for the …

A bstract The “quantum complexity” of a unitary operator measures the difficulty of its
construction from a set of elementary quantum gates. While the notion of quantum …

The exponential growth rate of non-polynomially growing subgroups of GLrf is conjectured
to admit a uniform lower bound. This is known for non-amenable subgroups, while for …

The main purpose of these lecture notes is to present Gromov's theorem on groups of
polynomial growth, which is one of the milestones in the theory of infinite groups. The idea of …

We prove curvature-free versions of the celebrated Margulis Lemma. We are interested by
both the algebraic aspects and the geometric ones, with however an emphasis on the …