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 …

In the last? fteen years two seemingly unrelated problems, one in computer science and the
other in measure theory, were solved by amazingly similar techniques from representation …

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth
studies the distribution of subgroups of finite index in a group as a function of the index. In …

The first part of this paper surveys generating functions methods in the study of random
matrices over finite fields, explaining how they arose from theoretical need. Then we …

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 …

For each finite simple group G there is a conjugacy class CG such that each nontrivial
element of G generates G together with any of more than 1/10 of the members of CG …

We present a" Practical" algorithm to construct random elements of a finite group. We
analyse its theoretical behaviour and prove that asymptotically it produces uniformly …

Let G be a finite simple group and let S be a normal subset of G. We determine the diameter
of the Cayley graph Γ (G, S) associated with G and S, up to a multiplicative constant. Many …

We derive a new bound for the minimal degree of an almost simple primitive permutation
group, and settle a conjecture of Cameron and Kantor concerning the base size of such a …

The study of fixed point ratios is a classical topic in permutation group theory, with a long
history stretching back to the origins of the subject in the 19th century. Fixed point ratios …