Braid groups and the Temperley-Lieb algebras
I am an American postdoctoral mathematician. My current position is a Research Fellow at Monash University under the supervision of Professor Jessica Purcell and Professor Daniel Matthews.
I completed a Ph.D. in the Spring of 2022 from The George Washington University under the supervision of Professor Jozef H. Przytycki.
I am a member of AMS, AustMS, and Women in Maths SIG.
I am interested in low-dimensional topology; studying 3- and 4-manifolds via Dehn surgery, Dehn fillings, hyperbolic knot theory, and 3-manifold invariants. In particular, I am interested in the relationship between quantum invariants of knots and 3-manifolds as well as their relationship to hyperbolic geometry via the AJ conjecture and volume conjecture as well as the relationship between Dehn surgery and 4-manifolds via the Generalized property R conjecture.
Furthermore, I am interested in diagrammatic algebras and the connection between Gram determinants in knot theory and statistical mechanics.