Research/Writing
Research/Writing
My current research interests are in geometric group theory. In particular, I am interested in studying the geometry of the mapping class group equipped with the word metric. I am also interested in applying topological techniques to complex dynamical problems.
The transitivity of Hurwitz classes of post-critically finite quadratic branched covers with R. Winarski.
Fibered 3-manifolds and Veech groups with C. J. Leininger, K. Rafi, N. Rouse, and E. Shinkle (Accepted to Algebraic & Geometric Topology).
The grand arc graph with A. Bar-Natan Mathematische Zeitschrift. 305(20), 2023.
Asymptotic dimension of big mapping class groups with C. Grant and K. Rafi (Submitted).
Automorphisms of the fine curve graph with A. Long, D. Margalit, A. Pham and C. Yao (Accepted to Transactions of the American Mathematical Society).
Stable specific torsion length and periodic mapping classes with E. Field. Topology and its Applications. 314(1):108134, 2022.
Finite image homomorphisms of the braid group and its generalizations with N. Scherich. Glasgow Mathematical Journal. 65(2), 430-445, 2023.
A construction of pseudo-Anosov homeomorphisms using positive twists. Algebraic & Geometric Topology. 23(4), 1601-1639, 2023.
Geodesics in the mapping class group with K. Rafi. Algebraic & Geometric Topology. 21(6), 2995–3017, 2021.
A combinatorial approach to solving nested recursions with non-monotonic solutions with M. Sunohara and S. Tanny. Journal of Difference Equations and Applications. 25(4), 1-23, 2019.
Constructing new families of nested recursions with slow solutions with A. Isgur, R. Lech, S. Moore, S. Tanny and Y. Zhang. SIAM Journal on Discrete Mathematics. 30(2), 1128-1147, 2016.
In Summer of 2022, I participated in the PIMS Math^Industry Workshop. The following preprint consists of the progress my team made over the two weeks we had to work on an industry related problem.
Locating Man-Made Objects in Vegetation from Aerial Multispectral Imagery with B. Joshi and H. Kohut.