Skeletons, degenerations, and Gromov—Witten theory

Non-archimedean analytic geometry provides a precise geometric connection between tropical curve counting and logarithmic Gromov-Witten theory. This framework leads to a simple new description of the algebraic moduli space of rational curves in toric varieties with prescribed contact orders. Applications include a new proof of Nishinou and Siebert’s tropical curve counting theorems and a new result on the structure of the tropical rational double Hurwitz cycle. Time permitting, I will explain how these ideas lead to a new perspective on the realization problem for embedded tropical curves in higher genus.