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 (2026) - J. London Math. Soc. 114(2), e70664. [Journal] [arXiv]
Writeups
This section contains writeups and other expository articles.
- A Trace-Path Integral Formula over Function Fields (p. 12) - Report for the Oberwolfach Workshop 2617 "Low-dimensional Topology and Number Theory"
- 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.