# Research

Research

My research is in low-dimensional topology under the guidance of Ina Petkova. I am currently focusing mostly on tangle Floer homology and combinatorial versions of knot Floer homology. I also work on connections with Khovanov homology, and applications to contact topology. My current research statement can be seen here.

Publications and Pre-prints
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)

Prior Work

My first year of graduate school I was very fortunate to be involved in a project on Hilbert modular forms. I helped compute canonical graded rings of parallel weight HMFs, and specialized Siegel modular forms/Igusa invariants to these spaces.

As an undergraduate, my REU research was focused on commutative algebra; namely the level of control over the generic formal fiber of complete local rings.