#  Research 

 



## **Publications and Preprints**

1. [On two notions of total positivity for generalized partial flag varieties of classical Lie types](https://arxiv.org/abs/2410.11804) - with G. Barkley, J. Boretsky, and C. Eur (submitted)
2. [Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes](https://arxiv.org/abs/2405.00778) - with J. Brakensiek, M. Dhar, S. Gopi, and M. Larson (submitted)
3. [Quotients of Special Classes of Positroids](https://arxiv.org/abs/2311.05340) - with Z. Chen, Y. Fei, Y. Sun, and Y. Zhang (submitted)
4. [Quantum Bruhat Graphs and Tilted Richardson Varieties](https://arxiv.org/abs/2309.01309) - with S. Gao and Y. Gao (in preprint)
5. [Balanced Shifted Tableaux](https://arxiv.org/abs/2203.12492) - with S. Gao and Y. Gao (Discrete Mathematics, 2024)
6. [Sandpile Groups of Cayley Graphs over F\_2^r](https://arxiv.org/abs/1912.06919) - with C. H. Yuen, J. Marx-Kuo, and V. McDonald (Communications of Algebra, 2024)
7. [Acyclic Orientations and the Chromatic Polynomial of Signed Graphs](https://arxiv.org/abs/2209.01303) (submitted)
8. [Virtual Complete Intersections in P1 \\times P1](https://arxiv.org/abs/1905.09991) - with Y. Li, M. Loper, and A. Mattoo (Journal of Pure and Applied Algebra, 2021)
9. [Generating Functions for f-vectors and the cd-index of Weight Polytopes](http://www-users.math.umn.edu/~reiner/REU/GaoMcDonald2018.pdf) - with V. McDonald (REU report)

## **Talks and Posters**

1. Quantum Bruhat Graphs and Tilted Richardson Varieties - Cornell Discrete Geometry and Combinatorics Seminar, Ithaca NY, Apr 2024 ([slides](/file_url/116))
2. A Tale of Three Matroids - AMS New England Graduate Student Conference, Providence RI, Apr 2024 ([slides](/file_url/114))
3. Pecha Kucha ([video](https://youtu.be/yJyq7Om--Ls?si=y_-BsBsQJh0qFjjL)) - Richard P. Stanley Seminar in Combinatorics, Cambridge MA, Mar 2024 ([slides](/file_url/113))
4. A Tale of Three Matroids - Graduate Student Combinatorics Conference (GSCC), Pittsburg PA, Mar 2024 ([slides](/file_url/112))
5. Quantum Bruhat Graphs and Tilted Richardson Varieties - UCSD Combinatorics Seminar, San Diego CA, Feb 2024 ([slides](/file_url/111))
6. Quantum Bruhat Graphs and Tilted Richardson Varieties - Richard P. Stanley Seminar in Combinatorics, Cambridge MA, Dec 2023 ([slides](/file_url/110))
7. Quantum Bruhat Graphs and Tilted Richardson Varieties - UIUC Algebra, Geometry, Combinatorics Seminar, Champaign IL, Nov 2023 ([slides](/file_url/109))
8. Quantum Bruhat Graphs and Tilted Richardson Varieties - Brandeis Combinatorics Seminar, Waltham MA, Oct 2023 ([notes](/file_url/108))
9. Quantum Bruhat Graphs and Tilted Richardson Varieties - University of Minnesota Twin Cities Combinatorics Seminar, Minneapolis MN, Sep 2023 ([slides](/file_url/107))
10. Riemann-Roch on Graphs - Harvard Trivial Notions Seminar, Cambridge MA, Apr 2023 ([notes](/file_url/106))
11. Balanced Shifted Tableaux - Graduate Student Combinatorics Conference (GSCC), St. Louis MO, Mar 2023 ([slides](/file_url/105))
12. Balanced Shifted Tableaux - Combinatoire Enumerative et Analytique, Paris France, Oct 2022 ([slides](/file_url/104))
13. The Sandpile Group of Cayley Graphs of F2^r - University of Vermont Combinatorics Seminar, Burlington VT, Sep 2022 ([notes](/file_url/103))
14. Toric Arrangements, Acyclic Orientations, and the Chromatic Polynomial of Signed Graphs - MIT-Harvard-MSR Combinatorics Seminar, Cambridge MA, Feb 2022 ([notes](/file_url/97))
15. Generating Functions for f-vectors of Simple Weight Polytopes - with V. McDonald, Joint Mathematics Meetings 2019, Baltimore MD, Jan 2019 ([slides](/file_url/98))
16. Virtual Complete Intersections of Points in P1 \\times P1 - with A. Mattoo and Y. Li, Joint Mathematics Meetings 2019, Baltimore MD, Jan 2019 ([slides](/file_url/100), [poster](/file_url/99))
17. The Sandpile Group of Cayley Graphs - with V. McDonald, Joint Mathematics Meetings 2019, Baltimore MD, Jan 2019 ([poster](/file_url/101))