Non-arithmetic lattices

A lattice is a discrete group of isometries of a space with finite volume quotient. For example, think of the lattice of points in the plane with integer x and y coordinates, whose quotient is a torus. A lattice is arithmetic if, in a rather sophisticated sense, discreteness follows from the discreteness of the integers in the reals. Non-arithmetic lattices are interesting and elusive objects. I will give an overview of the topic and then outline a joint project with Deraux and Paupert where we constructed the first new examples of non-arithmetic complex hyperbolic lattices to be found in more than 30 years.
 

Bio
https://maths.dur.ac.uk/users/j.r.parker/