I am a Junior Fellow at the Institute for Theoretical Studies at ETH Zürich in Switzerland. My mentor at ITS is Anna Beliakova. I completed my PhD in Mathematics in Spring 2021 at the George Washington University under the supervision of Józef H. Przytycki.
My research interests are in knot theory, low – dimensional topology, and algebraic and quantum invariants of manifolds. I focus primarily on the study of skein modules and skein algebras of 3 – manifolds and the Topological Quantum Field Theoretic description of the Witten – Reshetikhin – Turaev 3 – manifold invariant.
My current program of research largely constitutes four prongs. The first involves categorifying the Kauffman bracket skein module for lens spaces and S1 – bundles over surfaces, providing a nontrivial generalisation of Khovanov homology leading to homological invariants of links in these manifolds with arbitrary rings of coefficients.The second is about determining the structure of the Kauffman bracket skein module over the ring of Laurent polynomials. The third is devoted to relative Kauffman bracket skein modules, the Temperley-Lieb algebra, Gram determinants, and the coloured Jones polynomial. The fourth prong, which is related to the third, is devoted to the study of skein modules through the lens of hyperbolic geometry. This involves studying skein modules in connection to the volume conjecture and AJ conjecture.
I am the coauthor of a scholarly book on knot theory, in which I have written six chapters devoted to the study of 3-manifold topology and skein modules. The book will soon be published by Springer, Universitext. I am also a coauthor of two chapters in the Encyclopedia of Knot Theory, with Józef H. Przytycki and Helen Wong.