Areas of Interest
Combinatorics, Topology
Research
My research focuses on interactions between combinatorics and topology, particularly those involving oriented matroids, convex polytopes, and other concepts from discrete geometry. Much of my work involves combinatorial models for topological structures such as differential manifolds and vector bundles. The aims of such models include both combinatorial answers to topological questions (e.g., combinatorial formulas for characteristic classes), and topological methods for combinatorics (e.g. on topology of posets). I have also worked on applications of oriented matroids to data analysis in psychology.
Courses
Fall 2026
| Course |
Section |
Title |
Schedule |
Room |
| Math 330 |
04 |
Number Systems |
MWF 1:30–3:00
|
WH-329
|
Ph.D. Students
-
Stefan Viola,
Summer, 2026
— On Matroids over the Triangle Hyperfield
-
Olakunle Abawonse,
Spring, 2022
— On the topology of flags of oriented matroids & spaces of flattenings of spheres
-
Ulysses Alvarez,
Spring, 2022
(Co-advisor:
Ross Geoghegan)
— On the topology of corank 1 tropical phased matroids
-
Christopher Eppolito,
Summer, 2022
(Co-advisor:
Thomas Zaslavsky)
— Matroids: Mystic Monoliths, Meta Missiles, and Myopic Meadows
-
Ting Su,
Fall, 2018
— Extensions of Matroids Over Tracts and Doubly Distributive Partial Hyperfields
-
Amanda Ruiz,
Summer, 2013
— Realization Spaces of Phased Matroids
-
Leandro Junes,
summer, 2008
— Duality of Higher Order Non-Euclidean Property for Oriented Matroids
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