Course description: The goal of this reading seminar is to go through Part A ("p-adic analysis and Lie groups") of Schneider's book. This develops the theory of p-adic Lie groups from scratch; it starts from differentiability, locally analytic functions, then defines manifolds and tangent spaces -- all in the context of a non-archimedean field. The last third introduces Lie groups, Lie algebras, and gives various descriptions of the universal enveloping algebra. Part A should be of interest to anyone wishing to learn the basics of Lie groups. If there's sufficient interest, we hope to cover Part B ("the algebraic theory of p-adic Lie groups") in a sequel; which is an exposition of Lazard's theory of p-valuations and its number-theoretic applications to Iwasawa algebras etc. Depending on the number of active participants, each participant should expect to give ~3 talks. Let me know if you want to be added to the mailing list.
Instructor: Claus Sorensen, csorensen [at] ucsd [etcetera].
Meetings: Tue and Thu, 1-2 PM, in APM 7421. (First meeting Jan 8th.)Textbook: Primarily p-Adic Lie Groups (Springer, 2011) by Peter Schneider, available here.
Prerequisites: Will be kept to a minimum. Prior exposure to p-adics, manifolds, and universal enveloping algebras, will be useful -- but is strictly speaking not necessary.