Matthew Baker

collaborators

6 papers

math.AG2026

Elliptic matroids and modular curves

Matthew Baker

For $n \geq 4$ , let $T_{n}$ be the rank-3 matroid on $Z / n Z$ whose bases are the three-element non-zero-sum subsets. Let $X_{1} (n)^{\circ}$ denote the open subscheme of t…

math.CO2026

Lorentzian polynomials and matroids over triangular hyperfields 2: Analytic aspects

Matthew Baker, June Huh, Mario Kummer +1

Brändén and Huh showed that Lorentzian polynomials unify Hodge-Riemann relations in combinatorics: their supports are M-convex, and every M-convex set supports a Lorentzian polynom…

math.CO2026

A modern perspective on Tutte's homotopy theorem

Matthew Baker, Tong Jin, Oliver Lorscheid

We begin with a review of Tutte's homotopy theory, which concerns the structure of certain graph associated to a matroid (together with some extra data). Concretely, Tutte's path t…

math.CO2025

Lorentzian polynomials and matroids over triangular hyperfields 1: Topological aspects

Matthew Baker, June Huh, Mario Kummer +1

Lorentzian polynomials serve as a bridge between continuous and discrete convexity, connecting analysis and combinatorics. In this article, we study the topology of the space $\mat…

math.CO2025

The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids

Matthew Baker, Oliver Lorscheid, Zach Walsh +1

We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we sh…

math.AG2025

New building blocks for $F_{1}$ -geometry: bands and band schemes