Research
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.
Trees and Tanglegrams
"Decks of rooted binary trees," under review.
"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.
Permutations
"Moments of colored permutation statistics by conjugacy class," (with J. Campion Loth, M. Levet, S. Sundaram, and M. Yin), under review.
"Colored permutation statistics by conjugacy class," accepted to Séminaire Lotharingien de Combinatoire.
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), under review.
"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), accepted to 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.