I shall discuss an ongoing work with Sean Lawton and Shiv Parsad where our aim is to classify pairs of elements of SU(3,1) up to conjugacy.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050