Research

My research interests broadly include Algebraic Number Theory and Arithmetic Geometry, and my current research focuses on Arithmetic Topology. I am interested in arithmetic analogues of linking phenomena in topology. For example, I am interested in arithmetic invariants arising from Arithmetic Chern-Simons Theory as defined by Minhyong Kim and his collaborators, which can be used to define a notion of arithmetic linking numbers. I am also interested in triple symbols which can be viewed as the arithmetic analogue of milnor invariants, which are used in topology to detect links such as the Borromean Rings. I am currently thinking about arithmetic analogues of the path integral-trace formula that arises in Quantum Field Theory.

Papers

Please see also my arXiv, ORCiD, and Google Scholar profiles.

• A Trace-Path Integral Formula over Function Fields (arXiv) (submitted)

Writeups

This section contains writeups and expository articles on various mathematical topics.

• Persistent Homology (2022) - A group project as part of the GlaMS PhD Training, written jointly with Malthe Sporring and Adrián Doña Mateo.
• Deforming Galois Representations (2022) - This is my Cambridge Part III Essay (Master's Thesis), written under the supervision of Professor Jack Thorne.
• On the q-analogue of Kostant's Partition Function (2021) - A summary of my undergraduate summer project supervised by Dr. Rong Zhou.
• More to come!