Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Schottky Algorithms: Classical meets Tropical

Seminar | October 30 | 5-6 p.m. | 939 Evans Hall

 Lynn Chua, UC Berkeley

 Department of Mathematics

We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and, if so, to compute the curve and its canonical embedding. We offer solutions and their implementations in genus four, both classically and tropically. The locus of cographic matroids arises from tropicalizing the Schottky-Igusa modular form. We also discuss numerical approaches to the classical Schottky problem in genus 5.