I am a rising fifth year graduate student and teaching assistant at the George Washington University pursuing a PhD in Mathematics 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. I also study self – distributive structures, and their generalisations, whose axioms are motivated by the Reidemeister moves in knot theory. Quandles and racks are prime examples of such structures.
My current research involves categorifying the Kauffman bracket skein module for lens spaces and providing a nontrivial generalisation of Khovanov homology leading to homological invariants of links in lens spaces with arbitrary rings of coefficients.