Colin Crowley

I'm a fifth year graduate student at University of Wisconsin -- Madison. I will be on the job market in the fall.

My advisor is Botong Wang, and I'm interested in the intersection of algebraic geometry and combinatorics, especially matroid theory.

Email: cwcrowley (at) wisc (dot) edu

Office: 416 Van Vleck Hall, Madison WI, 53706

Papers

The Bergman fan of a polymatroid, with June Huh, Matt Larson, Connor Simpson, and Botong Wang. http://arxiv.org/abs/2207.08764.
Hyperplane arrangements and compactifications of vector groups. In preparation.

We give an axiomatic definition of matroid Schubert varieties as equivariant compactifications of vector groups which satisfy certain properties. This perspective has many parallels to the theory of toric varieties.

Regeneration Trees for Polynomial System Solving, with Jose Israel Rodriguez, Jacob Weiker, Jacob Zoromski. https://arxiv.org/abs/1912.04394.
A Module-Theoretic Approach to Matroids. With Noah Giansiracusa, Joshua Mundinger. arXiv: 1712.03440

Conferences and Summer Schools

Combinatorial, computational, and applied algebraic geometry. Seattle WA. June 2022.
Tropical Geometry -- MSRI Summer School. Moragan, CA. August 2022.

Open Problems in Algebraic Combinatorics. Minneapolis, MN. May 2022.

GradMoCCA: A graduate meeting on combinatorial commutative algebra. Minneapolis, MN. May 2022.

CA+ . Ames, IA. April, 2022.

CA+. Minneapolis, MN. October, 2021.

Arrangements at home. Virtual, 2020.

SIAM Conference on Applied Algebraic Geometry (AG19). University of Bern, Switzerland. July 2019.
Summer School on Randomness and Learning in Non-Linear Algebra. Max Planck Institute for Mathematics in the Sciences, Leipzig. July 2019.
Meeting on Applied Algebraic Geometry. Georgia Tech, Atlanta GA. April 2019.
Midwest Algebraic Geometry Graduate Conference. University of Illinois at Chicago. March 2019.

Talks and Presentations

Lefschetz hyperplane section theorem via Morse theory. Talk at UW Madison Matroids Seminar and Reading Group. January 2020.
"Matroid Bingo". A short introductory talk about matroids at the UW Madison AMS chapter seminar. November 2019
Hyperplane arrangements and maximum likelihood degree. Talk at UW Madison Matroids Seminar and Reading Group. December 2019.
A Module-Theoretic Approach to Matroids. Poster presentation at SIAM Conference on Applied Algebraic Geometry (AG19). July 2019.
Exposition of Riemann-Roch and Abel-Jacobi theory on a finite graph. Talk at the UW Madison Graduate Algebraic Geometry Seminar. April 2019.
Matroids and coding theory. Talk at the UW Madison Matroids Seminar and Reading Group. March 2019.
Matroid Polytopes. Talk at the UW Madison Matroids Seminar and Reading Group. February 2019.

Teaching and Mentoring

I was the graduate mentor for the Collaborative Undergraduate Research Lab (CURL).
I was an organizer for, and have given three lessons for, Madison Math Circles, an outreach program organized by the UW Math Department.