My general research area is combinatorics, grouped broadly into some areas below. In addition to natural follow-up problems to those shown, I am also researching Higher Bruhat Orders and reconstruction of tanglegrams.
Reflection Groups and Coxeter Groups
"Descents and flag major index on conjugacy classes of colored permutation groups without short cycles" (with M. Yin), under review.
"Descents and flag major index on conjugacy classes of Snr without short cycles" (with M. Yin), accepted to Séminaire Lotharingien de Combinatoire as part of the Proceedings for FPSAC 2025.
"Moments of colored permutation statistics by conjugacy class," (with J. Campion Loth, M. Levet, S. Sundaram, and M. Yin), published in Annals of Combinatorics.
"Colored permutation statistics by conjugacy class," published in Séminaire Lotharingien de Combinatoire as part of the Proceedings for FPSAC 2024.
Trees and Tanglegrams
"Reconstruction of caterpillar tanglegrams" (with A. Clifton, E. Czabarka, S. Loeb, U. Okur, L. Szekely, and K. Wicke), under review.
"Decks of rooted binary trees" (with A. Clifton, E. Czabarka, A. Dossou-Olory, S. Loeb, U. Okur, L. Szekely, K. Wicke) published in European Journal of Combinatorics.
"Characterizing planar tanglegram layouts and applications to edge insertion problems," published in Electronic Journal of Combinatorics.
"Sampling planar tanglegrams and pairs of disjoint triangulations" (with A. Black, A. McDonough, G. Nelson, M. Wigal, M. Yin, and Y. Yoo), published in Advances in Applied Mathematics.
"Planar tanglegram layouts and single edge insertion," published in Séminaire Lotharingien de Combinatoire as part of the Proceedings for FPSAC 2022.
Zero Forcing
"New Structures and their Applications to Variants of Zero Forcing and Propagation Time" (with L. Hogben, M. Hunnell, H. Schuerger, B. Small, and Y. Zhang), accepted to Electronic Journal of Combinatorics.
"Upper bounds for positive semidefinite propagation time" (with L. Hogben, M. Hunnell, H. Schuerger, B. Small, and Y. Zhang), published in Discrete Mathematics.
"Using Markov chains to determine expected propagation time for probabilistic zero forcing" (with Y. Chan, E. Curl, J. Geneson, L. Hogben, I. Odegard, and M. Ross), published in Electronic Journal of Linear Algebra.
I have also worked on some projects as a mentor for undergraduates in the Washington eXperimental Mathematics Laboratory. I was fortunate to have excellent groups of students, and our resulting papers are given below.
Characterizing Graphs with Small Boundary
"Characterizing graphs with at most four boundary vertrices" (with N. Chiem, W. Dudarov, C. Lee, and S. Lee), published in Journal of Combinatorics.
Extremal Closed Geodesics on the Torus
"Cosine sign correlation" (with S. Dou, A. Goh, M. Legate, and G. Pettigrew), published in Journal of Fourier Analysis and Applications.