Pure Mathematics Colloquium - Margulis regions for screw-parabolic maps

Dates

Tuesday, November 29, 2022 - 14:00 to 15:00

Speaker: John Parker (Durham University)

Abstract: A famous result of Margulis says that there is a universal constant only depending on dimension with the following property. If G is a discrete group of hyperbolic isometries and x is a point then the elements of G that displace x by a distance less than the constant generate a nilpotent group. 

The thin part of the quotient orbifold is the collection of points where this nilpotent group is infinite. In this talk I will discuss the shape of the thin part of a hyperbolic 4-manifold associated to a screw-parabolic map with irrational rotational part. This involves results from Diophantine approximation in rather surprising ways.