My research interests lie primarily in topological combinatorics and have connections to discrete geometry and commutative algebra. I am particularly interested in studying the interplay of various algebraic, topological, and combinatorial properties of simplicial complexes. I also study matching complexes, polytopes, and universal partial words.
These interactive graphics of a combinatorial cube with perpendicular opposing facets and a pentagon with its type cone illustrate some phenomena studied in my recent preprint "Minkowski summands of cubes."
I especially enjoy doing research with undergraduates, and my projects have aspects that are well-suited for student involvement. See my student research page for more information on this in particular.
Research articles
The symbol * indicates an undergraduate coauthor.
| A characterization of two-dimensional Buchsbaum matching complexes
with Fran Herr*, Legrand Jones II*, and Rowan Rowlands. Preprint. |
arXiv |
| Minkowski summands of cubes with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying. Bulletin of the London Mathematical Society, to appear. |
arXiv |
| Partition and
Cohen–Macaulay extenders with Joseph Doolittle and Alex Lazar. European Journal of Combinatorics, to appear. |
arXiv |
| Resolving Stanley's conjecture on k-fold acyclic complexes with Joseph Doolittle. Combinatorial Theory, to appear. |
arXiv
Sage code |
| Lattice polytopes from Schur and symmetric Grothendieck polynomials with Margaret Bayer, Su Ji Hong, Tyrrell McAllister, McCabe Olsen, Casey Pinckney, Julianne Vega, and Martha Yip. Electronic Journal of Combinatorics, 28 (2021), no. 2, 36pp. |
arXiv
Journal |
| Manifold matching complexes with Margaret Bayer and Marija Jelić Milutinović. Mathematika 66(4), 973–1002. (2020). |
arXiv
Journal |
| Higher nerves of simplicial complexes with Hailong Dao, Joseph Doolittle, Ken Duna, Brent Holmes, and Justin Lyle. Algebraic Combinatorics, Volume 2 (2019) no. 5, p. 803–813. |
arXiv
Journal |
| Universal partial words over non-binary alphabets with Corbin Groothuis, Cyrus Hettle, Brian Kell, Pamela Kirkpatrick, Rachel Kirsch, and Ryan Solava. Theoretical Computer Science 713, 56–65. (2018). |
arXiv
Journal |
| A non-partitionable Cohen–Macaulay simplicial complex with Art Duval, Caroline Klivans, and Jeremy Martin. Advances in Mathematics 299, 381–395. (2016). |
arXiv
Journal |
Selected talk slides
See my CV for a complete list of the conference, seminar, and colloquium talks I've given.
| Partition extenders, skeleta of simplices, and Simon's conjecture ECM Applied Combinatorial Topology Minisymposium |
Slides |
| Type cones and products of simplices AMS Special Session on Algebraic, Geometric and Topological Combinatorics |
Slides
Cube Type Cone |
| Manifold matching complexes AMS Special Session on Research from the Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics |
Slides |
| Resolving Stanley's conjecture on k-fold acyclic complexes AMS Special Session on Geometric and Topological Combinatorics |
Slides |