I'm a representation theorist. The idea is to take ideas from the modular representation theory of finite groups (relative projectivity and so on), and transfer the results to profinite groups. It's often not quite as simple as it seems though, so we specify that we only care about finitely generated modules, or that the modules are over the completed group algebra of a virtually pro-p group, or usually both. There are two papers at the moment:

The first is called 'Modular representations of profinite groups'. It has a characterisation of relatively projective modules over profinite groups, definitions and facts about vertices and sources (especially conjugacy), and a version of Green's indecomposability theorem. It also has loads of the sort of lemma you need over and over when you do this sort of thing. It's at the Journal of Pure and Applied Algebra.

The second, which relies heavily on the first, is called 'Green Correspondence for Virtually pro-p Groups'. The reason the correspondence looks a little different from standard is because the restriction functor basically has a bad attitude, so if you play with it and it does something horrific don't make out like I didn't warn you. The paper is available in the Journal of Algebra.

As is standard, the papers above assume quite a lot of background knowledge. If you're up for a few more pages of reading, my thesis has a substantial preamble, quoting prerequisite results and giving references for their proofs. Note the constrained acknowledgements!

Recently, Claude Cibils and I have been doing flat out category theory. It goes like this: Start with a small category B. A covering of B is a functor F from C to B that's a bijection on the "stars" around each object of C (so locally it looks like an isomorphism of categories). The category of coverings of B is a small category, and (fiddly details aside) it has a universal object! Even cooler: the (so-called "Galois") coverings of B can be constructed explicitly from the quotients of the fundamental groupoid of B. The paper is submitted. It's also ArXived here.

If you're interested in what I do, the best thing is to email me. My address can be found in the 'Contact Me' section. Granted I could just put it here, but then what would be the point of the 'Contact Me' section?