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.