The core material of the book should be accessible to third year students, requiring only a
basic acquaintance with group theory, metric spaces, and point-set topology. I tried to keep …

In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which
was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery …

It has been close to ten years since the publication of Green's influential survey Finite field
models in additive combinatorics [28], in which the author championed the use of high …

This collection of open problems has been circulated since 2018 when, encouraged by
Sean Prendiville, I prepared a draft for the Arithmetic Ramsey Theory workshop in …

Working within the framework of free actions of countable amenable groups on compact
metrizable spaces, we show that the small boundary property is equivalent to a density …

We study definably amenable NIP groups. We develop a theory of generics showing that
various definitions considered previously coincide, and we study invariant measures. As …

Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes
which have applications to many areas of mathematics. Typically, this topic is presented to …

This is a survey of methods developed in the last few years to prove results on growth in non-
commutative groups. These techniques have their roots in both additive combinatorics and …

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 …

In this article we introduce and study uniform and nonuniform approximate lattices in locally
compact second countable (lcsc) groups. These are approximate subgroups (in the sense of …