Since you have done representation theory, you should have a look at Persi Diaconis wonderful:
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.lnms/1215467407
(which can be downloaded freely from that link). It should contain a lot of possible projects!, P Diaconis often uses the frase " somebody should look into this ... " There is a lot which is undone there!