Research

Research

My primary research focus is on mentoring undergraduate work. This includes MQPs, WPI’s closest equivalent to a senior thesis, and other research projects. If you are interested in a project in knot theory, low-dimensional topology, or topological data analysis, get in touch! Or if you just want to chat to see if we have any overlapping interests, let me know.

Prior Work

My dissertation was in low-dimensional topology, focusing on the combinatorial and computational aspects of knot Floer homology. I also did an REU as an undergraduate in commutative algebra, and my first year of graduate school joined a project on Hilbert modular forms. An older version of my research statement from when I was on the job market in the fall of 2021 can be found here.

Publications and Pre-prints
On the invariance of the Dowlin spectral sequence (with Z. Winkeler)
On grid homology for lens space links: combinatorial invariance and integral coefficients
L-space knots with tunnel number $>1$ by experiment (with C. Anderson, K. Baker, X. Gao, M. Kegel, K. Le, K. Miller, S. Onaran, G. Sangston, A. Wood, and A. Wright), to appear in Experimental Mathematics
Controlling the generic formal fiber of local domains and their polynomial rings (with P. Jiang, A. Kirkpatrick, S. Loepp, and S. Mack-Crane)