Desmond Coles

activity

20182025

collaborators

8 papers

math.AG2025

Spherical tropical curves are balanced

Desmond Coles

One of the characterizing features of tropicalizations of curves in an algebraic torus is that they are balanced. Tevelev and Vogiannou introduced a spherical tropicalization map f…

math.AG2025

Towards the tropicalization of reductive groups

Desmond Coles, Martin Ulirsch

Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic zero carrying the trivial valuation. In this article we discuss two candidates…

math.AG2023

A construction of algebraizable formal models

Desmond Coles, Netanel Friedenberg

Let $X$ be a variety over a complete nontrivially valued field $K$ . We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedd…

math.CO2023

Locally finite completions of polyhedral complexes

Desmond Coles, Netanel Friedenberg

We develop a method for subdividing polyhedral complexes in a way that restricts the possible recession cones and allows one to work with a fixed class of polyhedron. We use these…

math.AG2022

Spherical tropicalization and Berkovich analytification

Desmond Coles

Let $X$ be a spherical variety. We show that Tevelev and Vogiannou's tropicalization map from $X$ to its tropicalization factors through the Berkovich analytification $X^{\text{an}…

math.AG2020

The moduli space of tropical curves with fixed Newton polygon

Desmond Coles, Neelav Dutta, Sifan Jiang +2

Given a lattice polygon, we study the moduli space of all tropical plane curves with that Newton polygon. We determine a formula for the dimension of this space in terms of combina…

math.AG2019

Tropically planar graphs

Desmond Coles, Neelav Dutta, Sifan Jiang +2

We study tropically planar graphs, which are the graphs that appear in smooth tropical plane curves. We develop necessary conditions for graphs to be tropically planar, and compute…

math.OA2018

The module embedding theorem via towers of algebras

Desmond Coles, Peter Huston, David Penneys +1

Jones and Penneys showed that a finite depth subfactor planar algebra embeds in the bipartite graph planar algebra of its principal graph, via a Markov towers of algebras approach.…