Ralph Morrison: Algorithms for Mumford curves over the p-adics

Let K be a non-Archimedean field, such as the field of p-adic numbers.  In the 1970's David Mumford considered the action of certain matrix groups on K, and showed that this action give rise to algebraic curves over K, now called "Mumford curves".  I'll begin with an introduction to these curves, and then discuss how to compute with them algorithmically.  The algorithms include finding abstract tropical skeleta, approximating Jacobians, and computing polynomial representations (and the corresponding tropicalizations).  This talk is based on joint work with Qingchun Ren.