I am a Visiting Assistant Professor in the Department of Mathematics at the University of California, Santa Barbara. My mentor at UCSB is Stephen Bigelow. Before this, I was a Junior Fellow at the Institute for Theoretical Studies at ETH Zürich in Switzerland under the mentorship of Anna Beliakova. I completed my PhD in Mathematics in 2021 at the George Washington University under the supervision of Józef H. Przytycki.
My research interests are in quantum topology, low – dimensional topology, and knot theory. I focus primarily on the study of skein modules and skein algebras of 3-manifolds and their connections to algebraic geometry, hyperbolic geometry, categorification, Topological Quantum Field Theories, Jones-Wenzl projectors, and cluster algebras. More recently I have taken up an interest in skein lasagna modules, which are generalisations of the Khovanov and Khovanov-Rozansky homology theories to 4-manifolds with links in their boundary. 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.
Research Interests
- Skein Modules and Algebras in 3D
- Categorification of Skein Modules
- Khovanov Homology
- Skein Lasagna Modules
- TQFTs
- The Volume Conjecture
- The AJ Conjecture
- Gram determinants
- Quandle and Yang-Baxter Homology
I am a coauthor of the scholarly book ‘Lectures in Knot Theory: An Exploration of Contemporary Topics’ which was published by Springer, Universitext on March 16, 2024. The book gives a fresh and solid treatment of topics in quantum topology, such as skein modules and Khovanov homology. I am also a coauthor of two chapters on quantum invariants and skein modules in the Encyclopedia of Knot Theory, with Józef H. Przytycki and Helen Wong.
The George Washington University has been hosting the biannual conference Knots in Washington since 1995. The website for the conference is https://blogs.gwu.edu/ccas-knotsinwashington/. Knots in Washington L (50) took place December 6-8, 2024.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
David Hilbert