I am in the penultimate year of my doctoral study in mathematical physics at Durham University, and looking for jobs starting around October. An up-to-date CV can be found on the top right corner of this page.

## Introduction

My undergraduate study was in physics at Imperial College, during which I gained extensive programming experience in Python and statistical data analysis skills. My doctoral research is on the interface of physics and mathematics, where I explore quantum field theories in connection with algebraic geometry.

While finishing up my thesis, I have been actively teaching myself quantitative finance and machine learning. Besides re-enforcing my statistical knowledge, it is fascinating to see the intimate connection between physics and finance. For example, the path integral approach in quantum physics can be applied to interpret stochastic calculus commonly used in options pricing.

I am a fast independent learner and an practical problem solver:

- My doctoral research requires a significant amount of algebraic geometry, which is one of the most abstract areas in mathematics. Despite of the lack of any formal mathematical training, I managed to grasp many of its core concepts and applied them in my research under two years.
- I love organisation and use an outlining software, OmniOutliner, to organise materials. To extend its usability for myself, I learned JavaScript in a few weeks and ended up building an open source project of a dozen plug-ins, which has been featured on their official website.

I love communicating and sharing my ideas. I regularly publish contents on my technology blog and educational YouTube channel. For example, I have made comprehensive tutorials on typesetting LaTeX and setting up KeePass on iPadOS.

## Research

My research interests lie broadly at the interface between theoretical physics and mathematics. In particular, I am captivated by the rich mathematical structures arising from supersymmetric quantum field theories. In the recent decades, the study of supersymmetric quantum field theories has proven to deliver striking insights into pure mathematics such as algebraic geometry, higher dimensional topology, non-commutative algebras, and representation theory.

The focus of my research has been in those mathematical structures arising from 3d supersymmetric quantum field theories. The research in analogous theories in 2d has shown substantial contributions to the development of mathematics, such as homological mirror symmetry, Gromov-Witten theory, and quantum cohomology. These 3d supersymmetric theories possess analogous but distinct structures. Therefore it is expected that the study in 3d supersymmetric quantum field theories would also yield fruitful results in similar areas. My research aims to explore these mathematical structures arising in one dimension higher, e.g., quantum/quasi-map K-theory.

As someone coming from a physics background, this branch of research has been proven to be a very challenging but rewarding journey. I have had to quickly grasp a wide variety of abstract mathematical concepts, including characteristic classes, moduli spaces, equivariant cohomologies, K-theory, intersection theory, and mirror symmetry. But it has been immensely satisfying to see how these mathematical structures emerge and interact with physics.

## Publication

*Mathew Bullimore, Andrea E. V. Ferrari, Heeyeon Kim, Guangyu Xu*, JHEP**05**, 116 (2022), The Twisted Index and Topological Saddles.

## Exposition

- Multivariate Jeffrey-Kirwan Residue and 3D Mirror Symmetry
- U(1)^K Chern-Simons Matter Gauge Theory
- Chern-Simons Terms from Determinant Line Bundles
- Supersymmetric Quantum Field Theory in Zero Dimension
- Arithmetic Construction of Number Systems
- Residue Theorem
- Singlet Lens Optimisation and Rainbow Simulation
- Geometry Optimisation of the Muon Production Target
- The Game of Entropy: Maxwellâ€™s Demon
- Investigation of Asymmetry in Particle Collisions
- A Scientific Theory of Music

## Project

I also have a tech nerd inside of me. Here are some of his projects.

- A blog and a YouTube channel on technology.
- JavaScript automation plug-ins for the outliner software, OmniOutliner.