Congrates and thanks a lot for the link mate. That's really useful. Yeah Ben is a really technical person. I met with him earlier this week, was pretty much lost after half an hour. Will try to hang in there and see how I go.
Well in summer research you are not expected to cook up new stuff (of course that would be bloody awesome). Depending on your choice of topic and supervisor, you may study a mathematical text thoroughly, understand a few journal papers, and perform some numerical computations if required. These are not as trivial as it sounds, a lot of the stuff you learn will be cutting-edge and won't be found in any undergraduate course. The total workload is similar to two 4th year courses (that's my estimate). There are a few brief summaries of past projects on the following website
http://www.ice-em.org.au/students.html#scholarship
Don't worry John will tell you what to do. He's quite flexible and funny at times. He's specialised in saddlepoint approximations, genetics models and canonical nalysis. He must have other research interests as well (every prof does). Yes Usyd is probably the strongest group in stats theory in the Sydney area. I am not too sure about the specific strengths though, everyone is doing different things. It's under a transition phase at the moment, a few senior people just retired and new people are coming in all the time.
There were 7 students doing stats honours this year, which is considered to be the biggest group in recent years (an outlier so to speak). There are probably a dozen or so stats majors in third year this year. It's not a very popular subject nationwide, which is quite ashamed.