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 This has all kind of been superceded by some other ideas due to Coleman, Stevens and myself, and so I will almost certainly never attempt to publish this paper.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.

automorphic_forms_for_compact_groups.pdf

automorphic_forms_for_gl1.pdf

automorphic_forms_for_gl2_over_Q.pdf

automorphic_forms_over_function_fields.pdf

dimension_of_spaces_of_eisenstein_series.pdf

epsilon_constants.pdf

examples_of_hida_families.pdf

explicit_formulae_for_coeffts_of_char_power_series_of_U.pdf

explicit_models_for_modular_curves.pdf

finite_flat_group_schemes_course.pdf

forms_of_reductive_algebraic_groups.pdf

fourier_transforms.pdf

grossencharacters.pdf

inductive_proof_of_fundamental_theorem_of_arithmetic.pdf

notes_on_boutot_carayol.pdf

notes_on_elliptic_curves_over_finite_fields.pdf

ribets_use_of_the_congruence_subgroup_property.pdf

the_adjoint_functor_theorem.pdf

what_does_a_general_unitary_group_look_like.pdf

why_is_an_ideal_class_group_a_tate_schaferevich_group.pdf

automorphic_forms_short_course.pdf

cases_of_kilfords_thesis.pdf

computing_group_cohomology_on_a_computer.pdf

definition_of_group_cohomology_and_homology.pdf

Euclidean_domains_and_integers_of_number_fields.pdf

explicit_maass_forms.pdf

functoriality_of_satake_iso.pdf

gouveas_thesis_summary.pdf

group_schemes_of_order_p_squared.pdf

harish_chandra_homomorphism.pdf

hodge_tate_theory.pdf

hodge_theory_for_buzzards.pdf

infinite_galois_theory.pdf

inflation_restriction.pdf

inner_twists.pdf

level_raising_on_shimura_curves.pdf

local_langlands_for_gl2R.pdf

local_langlands_general_abelian_case.pdf

local_langlands_normalisation.pdf

model_theory_notes.pdf

modular_forms_of_half_integral_weight.pdf

modular_symbols.pdf

moduli_spaces_for_abelian_varieties_over_C_part_2.pdf

moduli_spaces_for_abelian_varieties_over_C.pdf

non-paritious_hmf_example.pdf

note_on_l_group_of_u2.pdf

notes_on_classical_principal_series_for_glnqp.pdf

notes_on_mod_p_local_langlands.pdf

notes_on_robba_ring.pdf

notes_on_weil_conjectures.pdf

notes_on_X0N.pdf

old_introductory_notes_on_local_langlands.pdf

old_notes_about_computing_modular_forms_on_def_quat_algs.pdf

pendulums_and_elliptic_curves.pdf

representations_of_real_reductive_groups.pdf

representations_of_real_reductive_groups_short_course.pdf

siegel_modular_forms_notes.pdf

slopes_theorems_and_counterexamples.pdf

summary_of_first_bit_of_jacquet_langlands.pdf

tannakian_categories_notes.pdf

trivial_remarks_about_tori.pdf

unitary_groups_basic_definitions.pdf

weight_one_eisenstein_series.pdf

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