Colin Crowley
I'm an RTG postdoc at the University of Oregon, working with Nick Proudfoot. For the 2024-25 academic year I'll be participating in the special year on algebraic and geometric combinatorics at the IAS.
I'm interested in the intersection of algebraic geometry and combinatorics, especially matroid theory. My advisor was Botong Wang.
Email: crowley (at) uoregon (dot) edu
Papers
Toric varieties modulo reflections, with Tao Gong and Connor Simpson. https://arxiv.org/abs/2410.14653
Polymatroid Schubert varieties, with Connor Simpson and Botong Wang. https://arxiv.org/abs/2410.10552
Hyperplane arrangements and compactifications of vector groups. http://arxiv.org/abs/2209.00052
The Bergman fan of a polymatroid, with June Huh, Matt Larson, Connor Simpson, and Botong Wang. http://arxiv.org/abs/2207.08764.
Regeneration Trees for Polynomial System Solving, with Jose Israel Rodriguez, Jacob Weiker, and Jacob Zoromski. https://arxiv.org/abs/1912.04394.
A Module-Theoretic Approach to Matroids. With Noah Giansiracusa, and 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
Introduction to Tropicalization Talk at UW Madison Graduate Algebraic Geometry Seminar. March 2022.
Introduction to Geometric invariant theory. Talk at UW Madison Graduate Algebraic Geometry Seminar. November 2021.
Introduction to Newton–Okounkov bodies. Talk at UW Madison Graduate Algebraic Geometry Seminar. February 2021.
Lefschetz hyperplane section theorem via Morse theory. Talk at UW Madison Graduate Algebraic Geometry Seminar. 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 Madison Math Circles, an outreach program organized by the UW Math Department.