Research Statement
Papers
- Skein Theory of Affine ADE Subfactor Planar Algebras Thesis, in preparation.
- Skein Theory of Affine A Subfactor Planar Algebras
Preprint on arXiv. arxiv.org/abs/2410.05519 - A Determinant Formula of the Jones Polynomial for a Family of Braids
with Derya Asaner, Sanjay Kumar, Andrew Pease, and Anup Poudel
Submitted. arxiv.org/abs/2408.13410
Projects in Progress
- Nuclear Dimension of Crossed Products by Hilbert Bimodules over Commutative C*-algebras with Marzieh Forough, Zahra Hassanpour-Yakhdani, Ja A Jeong, Preeti Luthra, and Karen Strung
- A Skein Theory for Nichols Hopf Algebras with Alex Bisnath and Quinn 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 with not only 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.