I am broadly interested in knot theory and low-dimensional topology. Currently, my primary focus is on questions related to the Cosmetic Crossing Conjecture (Problem 1.58 from Kirby's list) and, more broadly, cosmetic Dehn surgery on 3-manifolds. Here is my new (as of August 2019) paper in this direction:
Cosmetic n-tangle replacements on fibered knots
Here is my thesis, which concerns the study of fibered links and unknotting operations on knots in the 3-sphere which extend to minimum-genus Seifert surfaces. The material contained in Chapter 4 is currently being refined into a more concise paper, in which one of the main theorems will be strengthened. It addresses a question posed by Baader and Dehornoy in their paper Trefoil Plumbing.