Brief introduction to metric geometry of p-adic number and to C-valued analysis on them

The seminar will take form of a very brief introduction to p-adic numbers themselves and to some basic facts on the topology and other geometric features of Qp, the space of p-adic numbers. A brief introduction to elements of C-valued analysis over Qp will follow touching the theory of generalized functions on Qp, Fourier analysis, the theory of pseudo-differential operators, and, as an ultimate goal with applications in mind, elements of diffusion and Schrödinger-like equations on Qp. The number theoretic aspects, algebraic aspects, or Qp-valued analysis will not be touched at all. Most results will simply be announced without demonstration.