I gave a course on classical representation theory of p-adic groups and promised the audience that I would put my TeX notes on the web. Here are the notes.
I wanted to understand the (very!) basic theory and some elementary examples of moduli spaces of abelian varieties with PEL structure, over the complexes. So I wrote some notes, which are here.
I found myself continually being asked what the local Langlands conjectures were, for some reason, once, so I wrote some notes on GL_2, inspired by a course that Richard Taylor once gave in Caltech in 1992. Stuff about local Langlands is here (note: these notes were written in 1998 before the proof of the Local Langlands conjectures for GL(n) was announced) and stuff about the Jacquet-Langlands correspondence for definite quaternion algebras is here.
A short note about an elementary construction of p-adic families of eigenforms (in a weak sense) for definite quaternion algebras is here. This has all kind of been superceded by some other ideas due to Coleman, Stevens and myself, and so I will almost certainly never attempt to publish this paper. The problem is that this paper only proves continuity, not analyticity, of the families.
My thesis is here, but it's not really the kind of thing that you want to read, it's rather wordy. It will perhaps one day appear as a few shorter papers.
Added Feb 2012 and April 2012: more notes -- you'll have to guess what they're about from the titles. Sorry.
Important note: All this stuff has never been submitted anywhere and so has never been refereed. Note also that some of these notes were written a long time ago, when I knew even less than I know now. Read at your own risk :-) and comments welcome.
Yves Maurer, a former undergraduate at Imperial College, once did some calculations on the zeros of certain p-adic L-functions, for an undergraduate project. His work has never been published, and in fact after writing up he realised a much more efficient way of approaching the problem, which would have enabled him to do his computations an order of magnitude more quickly. On the other hand, his write-up contains, for example, the first 1000 terms of the (unique) zero of the 37-adic zeta function, and I know of no other reference for things like this. Yves kindly let me put a link up to his project, it's here. A brief explanation (written by me) of the more optimal approach, which Yves explained to me after he had finished the project, is here.
Dan Snaith was a PhD student of mine, and he wrote his thesis on overconvergent
Siegel modular forms from a cohomological viewpoint. Note that some of the ideas
in the thesis are also present, either implicitly or explicitly, in work of Tilouine
and his co-authors, and also in work of Emerton. One thing I like about Dan's write-up
is that it really does give a very hands-on approach to the subject.
The main ideas are: following Chenevier's approach for GL_n he p-adically interpolates the algebraic representations of the symplectic group GSp_2n, and hence defines cohomological overconvergent automorphic forms for these symplectic groups. He then restricts to the case n=2 and constructs analogues of Coleman's theta^(k-1) map---one for each element of the Weyl group of Sp_4.
Dan's thesis is here, but he doesn't intend to publish it, because as well as writing lovely mathematics, he also found that he could write lovely music.
Dan Jacobs was also a PhD student of mine and at the time of writing (2004!) there has been some recent interest in his thesis, which is here. Dan explicitly computed a chunk of the eigencurve associated to a certain definite quaternion algebra, and found (as in Buzzard-Kilford, but historically prior to this) that it was a disjoint union of copies of weight space. The thesis is (in my opinion) very clearly-written and might well be of use to people who want to learn about such things.
Owen Jones was a PhD student of mine who wrote a thesis on theta maps for locally analytic representations. His thesis is here.
Yukako Kezuka was an MSc student at Imperial College in 2011-2012. Her MSc project was on the class number one problem, and her write-up is very readable; it develops essentially all of the theory that one needs to solve the problem, following the Heegner/Stark approach. The thesis is here.
Anca Ciobanu did a BSc project with me on group cohomology in low degree in Lean, and proved the 7 term long exact sequence. Her project is here.
Kevin Buzzard is his-last-name at ic.ac.uk