I received my PhD in Mathematics from the University of Sheffield in 2015, under the supervision of Prof. Neil Dummigan. After, I was a Heilbronn Research Fellow at the University of Bristol until 2022, working on research of both theoretical and practical importance in Mathematics.
My main area of research is (Algebraic) Number Theory. In particular, I work on problems that involve a wide range of objects, from extremely explicit to mind bogglingly abstract:
I like problems that are explicit (e.g. How do I compute this thing? How do I count these things? How do I tell whether two of these things are different?), but I also like much deeper problems (e.g. Does what I just did apply for more general families of automorphic form/Galois representations? How does what I just did fit into the general framework of the Langlands program? Have I just proved a special case of the Bloch-Kato conjecture?). Some of my work is motivated by deep conjectures in Mathematics, and the practical need to compute explicit evidence for these.
Recently, I have been working on a couple of projects relating to Combinatorial Probability. In particular, I have studied a specific family of Markov chains called Interacting Particle Systems. These are useful in Statistical Mechanics and Physics (e.g. they can be used to model traffic flow). By comparing dynamics/probability measures on such systems one can often prove q-series identities of combinatorial significance (e.g. the famous Jacobi triple product identity).
I am currently thinking about how my research can be useful in the real world (e.g. Cybersecurity, Cryptography and Quantum Computation). Have any ideas about this? Send me an email!