UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

January 28, 2014

939 Evans Hall

3:45PM: Algorithms for Mumford curves over the p-adics

Ralph Morrison

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 minimal skeleta, approximating Jacobians, and computing polynomial representations (and the corresponding tropicalizations). This talk is based on joint work with Qingchun Ren.

5:00PM: Six points and the outer automorphism of S6

David Berlekamp

The invariant theory of six points in projective space can be nicely described using a pleasant description of the outer automorphism of S6. This is work of Howard, Millson, Snowden, and Vakil.

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