We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is
naturally identified with the moduli space of extended tropical curves, and that this is …

We study the topology of a space $\Delta _ {g} $ parametrizing stable tropical curves of
genus $ g $ with volume $1 $, showing that its reduced rational homology is canonically …

We contribute to the foundations of tropical geometry with a view toward formulating tropical
moduli problems, and with the moduli space of curves as our main example. We propose a …

Let $ A=(a_1,\ldots, a_n) $ be a vector of integers which sum to $ k (2g-2+ n) $. The double
ramification cycle $\mathsf {DR} _ {g, A}\in\mathsf {CH}^ g (\mathcal {M} _ {g, n}) $ on the …

This article is a sequel to [14]. We study a space g, n of genus g stable, n-marked tropical
curves with total edge length 1. Its rational homology is identified with both top-weight …

We study the relationship between tropical and classical Hurwitz moduli spaces. Following
recent work of Abramovich, Caporaso and Payne, we outline a tropicalization for the moduli …

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 construct the moduli space for equivalence classes of n-pointed tropical curves of genus
g, together with its compactification given by weighted tropical curves, and establish some of …

We study the locus of tropical hyperelliptic curves inside the moduli space of tropical curves
of genus g. We define a harmonic morphism of metric graphs and prove that a metric graph …

We show that a certain locus inside the moduli space $ M_g $ of hyperbolic surfaces, given
by surfaces with" sufficiently many" short geodesics, is a classifying space of the handlebody …