2 citations · 3 across the 8 of their papers we have counts for
8 papers
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…
Elliptic matroids and modular curves
Matthew Baker
For , let be the rank-3 matroid on whose bases are the three-element non-zero-sum subsets. Let denote the open subscheme of t…
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 a certain graph associated to a matroid (together with some extra data). Concretely, Tutte's path…
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…
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…
New building blocks for -geometry: bands and band schemes
Matthew Baker, Tong Jin, Oliver Lorscheid
We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sen…
Foundations of matroids -- Part 2: Further theory, examples, and computational methods
Matthew Baker, Oliver Lorscheid, Tianyi Zhang
In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks. For example, we show that…
On a theorem of Lafforgue
Matthew Baker, Oliver Lorscheid
We give a new proof, along with some generalizations, of a folklore theorem (attributed to Laurent Lafforgue) that a rigid matroid (i.e., a matroid with indecomposable basis polyto…