Let C be a nonempty class of finite groups this will always mean that C contains all the
isomorphic images of the groups in C. Define a pro—C group G as an inverse limit G=\lim i …

We introduce and study the notions of hyperbolically embedded and very rotating families of
subgroups. The former notion can be thought of as a generalization of the peripheral …

The topic of this book is 3-manifold groups, that is, fundamental groups of compact 3-
manifolds. This class of groups sits between the class of fundamental groups of surfaces …

Expander graphs are highly connected sparse finite graphs. They play an important role in
computer science as basic building blocks for network constructions, error correcting codes …

We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …

To those precious colleagues who can appreciate the goals of and connections to other
areas. To those who acknowledge the depth of what we already know from the absorbed …

After a forty-year lull, the study of word-values in groups has sprung back into life with some
spectacular new results in finite group theory. These are largely motivated by applications to …

Almost all primitive permutation groups of degree n have order at most [Formula: see text] or
have socle isomorphic to a direct power of some alternating group. The Mathieu groups …

We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold
associated to a representation of its fundamental group. We summarize their formal …

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken
Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a …