School of Mathematical Sciences

Constructing non-arithmetic lattices menu

Constructing non-arithmetic lattices

Speaker: 
John Parker (Durham)
Date/Time: 
Mon, 11/10/2010 - 17:30
Room: 
M103
Seminar series: 

A lattice L in a semisimple Lie group G is a discrete subgroup
of G for which the quotient L\G has finite volume. One may
construct lattices using number theory and such lattices are
said to be "arithmetic". Lattices that cannot be constructed
in this way are called "non-arithmetic" are hard to find.
In this talk we focus on the case where G=SU(n,1). The first
non-arithmetic lattices in SU(2,1) were constructed by
Mostow in 1980. Subsequently Deligne and Mostow found a
family of non-arithmetic lattices in SU(2,1) and a single
example in SU(3,1). In this talk I will outline a way of
generalising Mostow's method to find new examples in SU(2,1),
which are the first to be found since the work of Deligne and
Mostow.