My Interests:

I am mainly focussing on problems dealing with the quantitative arithmetic of varieties. In simple terms: I want to understand the number of rational solutions of bounded height to a set of polynomial equations asymptotically as the height grows toward infinity. In the past I have been particularly interested in such problems over function fields and number fields.

In the past I have done some research on Artin L-functions and Maass forms joint with Thomas Oliver. During my Master's project I investigated von Mangoldt functions attached to Galois representations of function fields, and how random matrix theory can help us to understand them in short intervals (article below). Here is an accessible summary about this project.

Aside from my pure mathematical research interests I am also doing research in quantitative finance and epidemiology.

Publications & Pre-prints:

• Cumulation, crash, coherency: A cryptocurrency bubble wavelet analysis (with W Frühwirt, L Weydemann, S Roberts), 2020, Finance Research Letters, pdf

• Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection (with WS Hart, RN Thompson, NJ Cunniffe, H Lee, N Nishiura), 2019, Epidemics

• Rational points on del Pezzo surfaces of low degree (with J Glas), 2024, arXiv

• Cubic forms over imaginary quadratic number fields and pairs of rational cubic forms (with C Bernert), 2023, arXiv, to appear in Transactions of the AMS

• On Artin's Primitive Root Conjecture for Function Fields over F_q (with E Waxman), 2023, Quarterly Journal of Mathematics, arXiv

• Systems of bihomogeneous forms of small bidegree, 2023, Acta Arithmetica, arXiv

• On a question of Davenport and diagonal cubic forms over F_q(t) (with J Glas), 2022, arXiv, to appear in Math. Annalen

• Variance of sums in short intervals and L-functions in F_q[t], 2021, J. Number Theory, arXiv

• Ratios of Artin L-functions (with T Oliver), 2021, J. Number Theory, arXiv

---