Papers
- "Skein Theory of Affine ADE Subfactor Planar Algebras" (thesis, in preparation)
- “Skein Theory of Affine A Subfactor Planar Algebras” (draft available upon request)
- "A Determinant Formula of the Jones Polynomial for a Family of Braids" with D. Asaner, S. Kumar, A. Pease, and A. Poudel (Submitted)
Projects in Progress
- "Nuclear Dimension of Crossed Products by Hilbert Bimodules over Commutative C*-algebras" with M. Forough, Z. Hassanpour-Yakhdani, J. Jeong, P. Luthra, and K. Strung
- "A Skein Theory for Nichols Hopf Algebras" with A. Bisnath and Q. Kolt
Research Overview
My advisor is Stephen Bigelow. My interests are in quantum algebra and quantum topology, which lie at the intersection of many fields of mathematics. I use tools primarily from higher category theory, knot theory, and subfactor theory to research quantum symmetry. Classical objects such as polygons and vector spaces are highly symmetric, and the language of groups helps describe these symmetries. However, objects from quantum mechanics have more complex symmetries that can no longer be captured through group theory. These quantum symmetries instead require the language of 2-categories. A 2-category is a higher category that not only has objects and morphisms, but also 2-morphisms between morphisms. These 2-categories are advantageous because they have a diagrammatic description which allows the use of topology, akin to knot theory. Just as groups are ubiquitous in mathematics, 2-categories are seen in a variety of subjects such as operator algebras, representation theory, topology, and mathematical physics.
I love discussing my research, so if you would like any more details on any of my projects, please feel free to email me.