PhD candidate in mathematics (University of Vermont), specializing in algebraic combinatorics and preparing for research-focused roles in AI and mathematical reasoning.
My research centers on matroid theory and its connections to geometry, topology, and Hodge-theoretic structures. I am particularly interested in training and evaluating AI systems on higher-level mathematics, proof-oriented reasoning, and abstract problem solving.
Research:
Tropical Geometry of Rado Matroids
Calum Buchanan, Richard Danner (2024)
[PDF (published)] ยท [arXiv]
Convex Geometry of Building Sets
Spencer Backman, Richard Danner (2024)
[arXiv]
Planar Ternary Graphs, Flag Spheres, and Delannoy Polynomials
Margaret Bayer, Richard Danner, Thiago Holleben, Marie Kramer, Yirong Yang (2025)
[arXiv]
Permutahedral and Stellahedral Morgan Models
Spencer Backman, Rick~Danner, Hsin-Chieh Liao, Crow Stephenson (2026)
[arXiv]