We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic
curves undergo tropical degenerations. Riemann's theta function becomes a finite …

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 …

AK 4-curve is a smooth proper curve X of genus 3 over a field with valuation whose
Berkovich skeleton Γ is a complete graph on four vertices. The curve X has 28 effective theta …

A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This
includes surfaces arising from special plane quartics that are singular or reducible. Lie and …

The solutions to the Kadomtsev–Petviashvili equation that arise from a fixed complex
algebraic curve are parametrized by a threefold in a weighted projective space, which we …

This article discusses the design of the Apprenticeship Program at the Fields Institute, held
21 August–3 September 2016. Six themes from combinatorial algebraic geometry were …

The Hirota variety parameterizes solutions to the KP equation arising from a degenerate
Riemann theta function. In this work, we study in detail the Hirota variety arising from a …

We discuss the classical problem of counting planes tangent to general canonical sextic
curves at three points. We determine the number of real tritangents when the curve is real …

1 Abelian tropical covers Page 1 Math. Proc. Camb. Phil. Soc.: page 1 of 22 1 doi:10.1017/S0305004123000518
Abelian tropical covers BY YOAV LEN Mathematical Institute, University of St Andrews, St …

We present an algorithm for computing the Berkovich skeleton of a superelliptic curve yn= f
(x) over a valued field. After defining superelliptic weighted metric graphs, we show that …