I do not currently have research projects for undergraduates. Check back later to see if I think any up.
I usually accept one graduate student per year. Deadlines for application are in January and you can apply as described here. We invite many candidates from the UK to interview at Oxford sometime in February. If you are not from the UK, dont' worry, apply the same way and we will still consider your application. We may ask to interview you by skype or phone. As many people know, if you are not from the UK, most british universities will have problems funding you. Our intended policy is that if you are a good candidate, and we make you an offer, we will find a way to fund you. However, if you come with your own money (grants or fellowships of some sort) that often makes it easier for us to accept you.
We tend to hire in the winter (jan-april). Please send applications and letters of recommendation as described here.
There are many other options for how to get funds to come here as a postdoc. For example, there is the prestigious All-Souls Postdoctoral Fellowship , the Glasstone Fellowship (particularly for women), the UK national Newton Fellowships , EPSRC Fellowships , and so forth. Sometimes the Oxford colleges have Junior Research Fellowships available as well (look here for announcements). NOTE: Some of these JRF positions are not enough money to live on and are meant to supplement other fellowships. There may also be fellowships available from your home country. In all cases, coming here as a postdoc must be approved by our entire group so make sure you send an official application etc.
See my web-page here . I can't be too specific as to what particularly projects I will be interested in at any given time. I do like to stay on the forefront of science which means that a project I think up right now will probably be no longer current in six months (or may have been scooped by other researchers in that time).
In order to get an idea of the kind of things I work on, I recommend reading
Some of my works are very abstract, like this one . Some are very closely related to experiment, like this one . Some are completely analytic, like this one . Some are very numerical, like this one . Most are somehow related to my main (topological) research directions, but a few are off in random directions, like these and these