Broadly, I like to think about knots and geometry, and especially their intersection. In particular, I like to think about hyperbolic manifolds and how we can use their geometric structure to obtain new information, such as considering deformations of those structures.
Currently, I am thinking about generalizations of bending deformations and how they can be used to address things like flexible manifolds and the Menasco-Reid conjecture.
Deformations of the Borromean Rings Link Complement, in preparation
As seen at GTA Philadelphia at Temple University May 2024
As seen at AMS-UMI in July 2024
As seen at Canaryfest 6.2 in July 2024 (Lightning Talk)
Fall 2020, I organized a learning seminar on the A-Polynomial.
Spring 2021, I organized a learning seminar on the Mapping Class Group.
Fall 2021, I organized the Junior Topology Seminar.
Summer 2022, I co-organizied a learning seminar on Pleated Surfaces and Eruptions, along with Fernando Camacho Cadena and Feng Zhu.
Fall 2022, I co-organized a learning seminar on Characteristic Classes, with Luis Torres and Aru Mukherjea.
Fall 2023, I organized a learning seminar on Lie Groups with Luis Torres.