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 lie in quantum topology, low – dimensional topology, and knot theory. My work focusses on skein modules and skein algebras of 3-manifolds and their interactions with algebraic geometry, hyperbolic geometry, categorification, Topological Quantum Field Theories, Jones-Wenzl projectors, and cluster algebras. I am also interested in emerging connections between my work and topological quantum computing. Recently I have begun exploring in skein lasagna modules, a framework that extends Khovanov and Khovanov-Rozansky homology theories to 4-manifolds with links in their boundaries.
Research Interests
- Skein Modules and Algebras in 3D
- Categorification of Skein Modules
- Khovanov Homology
- TQFTs
- Topological Quantum Computing
- Knot TheorySkein Lasagna Modules
- Diagrammatic Algebra
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