Tropical methods in the moduli theory of algebraic curves

TL;DR

This survey discusses recent advances in tropical and non-archimedean geometry that have provided new insights into the moduli spaces of algebraic curves and their Jacobians.

Contribution

It compiles and explains recent significant results in tropical and non-archimedean geometry related to algebraic curves and their moduli spaces.

Findings

New connections between tropical geometry and moduli theory

Enhanced understanding of Jacobians via tropical methods

Recent progress in non-archimedean approaches

Abstract

In recent years a series of remarkable advances in tropical geometry and in non-archimedean geometry have brought new insights to the moduli theory of algebraic curves and their Jacobians. The goal of this survey, an expanded version of my talks at the 2015 AMS symposium in algebraic geometry and at AGNES 2016, is to present some of the results in this area.