I am a mathematician who received my Ph.D. in Mathematics from the University of Vermont in 2026, where I worked in algebraic combinatorics under the supervision of Spencer Backman.
My research is in matroid theory and its connections to geometry, topology, and algebraic structures. More broadly, I am interested in how abstract ideas can be organized, explained, tested, and used to solve difficult problems.
I am currently exploring roles where rigorous reasoning, clear communication, and broad problem-solving ability are useful to a team. My background spans mathematical research, teaching, technical writing, data-oriented work, and hands-on building projects, including construction and stonework on the reconstruction of a 13th-century Spanish monastery in Vina, California. I enjoy work that involves learning quickly, building relationships, translating complex ideas, and helping a group make steady progress toward a shared goal.
Research:
Tropical Geometry of Rado Matroids
Calum Buchanan and Richard Danner. Discrete Mathematics Letters 14 (2024), 27–30. DOI: 10.47443/dml.2024.044.
[PDF (published)] · [arXiv]
Convex Geometry of Building Sets
Spencer Backman and Richard Danner. Convex Geometry of Building Sets. To appear in Order, 2026.
[arXiv]
Planar Ternary Graphs, Flag Spheres, and Delannoy Polynomials
Margaret Bayer, Richard Danner, Thiago Holleben, Marie Kramer, and Yirong Yang. Accepted pending final revisions, The Electronic Journal of Combinatorics, 2026.
[arXiv]
Permutahedral and Stellahedral Morgan Models
Spencer Backman, Rick~Danner, Hsin-Chieh Liao, Crow Stephenson, 2026.
[arXiv]