I am most intrigued by the interplay between topology and geometry. I spent a few years working on problems in hyperbolic knot theory and am now living in the world of contact topology. My advisor, Roger Casals, has a great introductory article in the AMS Notices about symplectic and contact geometry, which you can find here.
My recent work involves studying the Legendrian Contact DG-Algebra for certain classes of braid closures. This object has ties to braid varieties and cluster structures, and I'm particularly interested in the differences between the commutative and noncommutative differential graded algebras on the level of homology.
PUBLICATIONS AND PREPRINTS
"TG-hyperbolicity of composition of virtual knots" with Colin Adams. Comm. Anal. Geom. 32 (2024), no. 10, 2617–2671; MR4844960
"Augmented cellular alternating links in thickened surfaces are hyperbolic" with Colin Adams, Michele Capovilla-Searle, Darin Li, Lily Li, Jacob McErlean, Natalie Stewart, and Xiwen Wang. Eur. J. Math. 9 (2023), no. 4, Paper No. 100, 26 pp.; MR4654988
“Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition” with Colin Adams, Michele Capovilla-Searle, Darin Li, Lily Li, Jacob McErlean, Natalie Stewart, and Xiwen Wang. Preprint: arXiv:2111.06319
"Superbridge and Bridge Indices for Knots" with Colin Adams, Nikhil Agarwal, Rachel Allen, Tirasan Khandhawit, Rebecca Winarski, Mary Wootters. Journal of knot theory and its ramifications. Vol.30 no.2 (2021) arXiv:2008.06483