# London Algebra Colloquium abstract

## Beauville groups and surfaces

### Prof. Gareth Jones (Southhampton), 17th January 2013

#### Abstract

Beauville surfaces, of current interest to algebraic geometers, are 2-dimensional
complex algebraic varieties formed by factoring the cartesian product of two quasiplatonic
curves of genus at least 2 by the free action of a finite group, called a Beauville group.
A group is a Beauville group if and only if it is a quotient of hyperbolic triangle groups
in two essentially different ways. I shall give a survey of recent progress in this topic,
such as the result of Guralnick, Malle and others that every non-abelian finite simple group
other than A_{5} is a Beauville group, the description of the automorphism group
of a Beauville surface, and the explicit construction, extending examples due to Serre, of
arbitrarily large families of Galois conjugate but mutually non-homeomorphic algebraic varieties.