Let K be an algebraically closed, complete non-Archimedean field. The purpose of this
paper is to carefully study the extent to which finite morphisms of algebraic K-curves are …

We discuss linear series on tropical curves and their relation to classical algebraic geometry,
describe the main techniques of the subject, and survey some of the recent major …

We prove several lifting theorems for morphisms of tropical curves. We interpret the
obstruction to lifting a finite harmonic morphism of augmented metric graphs to a morphism …

We define d-gonal weighted graphs using “harmonic indexed” morphisms, and prove that a
combinatorial locus of M_ g contains ad-gonal curve if the corresponding graph is d-gonal …

In this work, we argue that the α'→ 0 α′→ 0 limit of closed string theory scattering
amplitudes is a tropical limit. The motivation is to develop a technology to systematize the …

We prove that the (divisorial) gonality of a finite connected graph is lower bounded by its
treewidth. Graphs for which equality holds include the grid graphs and the complete …

We study the moduli space of metric graphs that arise from tropical plane curves. There are
far fewer such graphs than tropicalizations of classical plane curves. For fixed genus g, our …

We construct a modular desingularisation of ℳ 2, n (ℙ r, d) main⁡. The geometry of
Gorenstein singularities of genus two leads us to consider maps from prestable admissible …

In this paper, we explore three combinatorial descriptions of semistable types of hyperelliptic
curves over local fields: dual graphs, their quotient trees by the hyperelliptic involution, and …

The image of the complement of a hyperplane arrangement under a monomial map can be
tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces …