Contents

pp v-vi

Introduction

pp vii-viii

Surveys

1 - Ergodic Ramsey Theory

pp 1-62

2 - Flows on homogeneous spaces

pp 63-112

3 - The variational principle for Hausdorff dimension

pp 113-126

4 - Boundaries of invariant Markov Operators: The identification problem

pp 127-176

5 - Squaring and cubing the circle – Rudolph's theorem

pp 177-184

6 - A survey of recent K-theoretic invariants for dynamical systems

pp 185-236

7 - Miles of Tiles

pp 237-258

8 - Overlapping cylinders: the size of a dynamically defined Cantor-set

pp 259-272

Research Papers

1 - Uniformity in the polynomial Szemérdi theorem

pp 273-296

2 - Some 2-d symbolic dynamical systems: Entropy and mixing

pp 297-306

3 - A note on certain rigid subshifts

pp 307-318

4 - Entropy of graphs, semigroups and groups

pp 319-344

5 - On representation of integers in Linear Numeration Systems

pp 345-368

6 - The structure of ergodic transformations conjugate to their inverses

pp 369-386

7 - Approximatiom by periodic transformations and diophantine approximation of the spectrum

pp 387-402

8 - Invariant σ-algebras for ℤd-actions and their applications

pp 403-414

9 - Large deviations for paths and configurations counting

pp 415-432

10 - A zeta function for ℤd-actions

pp 433-450

11 - The dynamical theory of tilings and Quasicrystallography

pp 451-474

12 - Approximations of groups and group actions, Cayley topology

pp 475-484