13 citations · 15 across the 8 of their papers we have counts for
12 papers
FIID Coloring Random Maps
Justin Hsu, Daniel Sium, Riley Thornton
We show that the percolation components on a square grid can be -colored as a factor of iid so that neighboring components get different colors. Above the critical probability,…
Compactness Principles for CSPs and the Axiom of Chocie
Anthony Li, Ishin Shan, Matthew Snodgrass +2
We can associate a compactness principle to the Constraint Satisfaction Problem (CSP) with constraint library . These principles were studie…
Topological weak containment
Riley Thornton
We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(…
Open Problems in Computability Theory and Descriptive Set Theory
George Barmpalias, Nikolay Bazhenov, Chi Tat Chong +11
These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Computability Theory and Descriptive Set Theory, June 16-20, 2025. The problems are…
Limits of sparse hypergraphs
Riley Thornton
We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs…
Factor of iid colorings of trees
Riley Thornton
We show that, for every , the 4-regular tree has an fiid 4-coloring where a given vertex is assigned the 4th color with probability at most . We also construct 5-colorings…
An algebraic approach to Borel CSPs
Riley Thornton
We adapt tools from the algebraic approach to constraint satisfaction problems to answer descriptive set theoretic questions about Borel CSPs. We show that if a structure $\mathcal…
Effectivization in Borel Combinatorics
Riley Thornton
We develop a flexible method for showing that Borel witnesses to some combinatorial property of objects yield witnesses. We use a modification the Gandy--Harrington…
Factor maps for automorphism groups via Cayley diagrams
Riley Thornton
We leverage a correspondence between group actions and edge-labelled graphs in two ways. First, we give a unified presentation of several folklore results connecting weak containme…
Orienting Borel Graphs
Riley Thornton
We investigate when a Borel graph admits a (Borel or measurable) orientation with outdegree bounded by for various cardinals . We show that for a p.m.p. graph , a measura…
The Homogeneous Spectrum of Milnor-Witt -Theory
Riley Thornton
For any field (of characteristic not equal to 2), we determine the Zariski spectrum of homogeneous prime ideals in , the Milnor-Witt -theory ring of . As a c…
Cubes and Their Centers
Riley Thornton
We study the relationship between the sizes of sets in where contains the -skeleton of an axes-parallel cube around each point in , generalizing the…