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 diving into the world of contact and symplectic geometry. I am currently thinking about Lagrangian fillings of Legendrian knots and am using the Legendrian contact DGA to do so. My advisor, Roger Casals, has a great introductory article in the AMS Notices about symplectic and contact geometry, which you can find here.
My most recent work involves studying the Legendrian Contact DG-Algebra.
PUBLICATIONS AND PREPRINTS
“TG-Hyperbolicity of Composition of Virtual Knots” with Colin Adams. To appear in Communications in Analysis and Geometry. Preprint: https://arxiv.org/abs/2110.09859
“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. European Journal of Mathematics 9, 100 (2023). Available at https://arxiv.org/abs/2107.05406
“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