Tropical methods in the moduli theory of algebraic curves
  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. 
Lucia Caporaso
math.AG