Associate Professor Daniel Delbourgo
Qualifications: PhD (Cambridge)
Administrative Roles: Graduate Advisor (Maths/Stats); Open Day Organisor (Maths/Stats); Maths Fees Scholarship Organisor; Member of the Academic Board; Postgraduate Research Committee Representative (FCMS)
Number theory is as relevant today as it was two millennia ago, with the advent of high-powered computing and cryptography.
Dr Delbourgo's research interests lie in the area of elliptic curves and modular forms.
His work applies ideas from classical Iwasawa theory and Galois representations, to study the arithmetic behaviour of invariants arising from these objects.
He is also interested in the special values of L-functions, and there is a rich vein of conjectures connecting these L-values with elements in K-groups.
Current PhD students: Hamish Gilmore; Qin Chao (Chris King);
Delbourgo, D., & Lei, A. (2017). Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions. The Ramanujan Journal, 43(1), 29-68. doi:10.1007/s11139-016-9785-1
Broughan, K., & Delbourgo, D. (2017). Corrigendum: A conjecture of De Koninck regarding particular values of the sum of divisors function. Journal of Number Theory, 180, 790-792. doi:10.1016/j.jnt.2017.04.010 Open Access version: https://hdl.handle.net/10289/11161
Delbourgo, D. (2016). Exceptional zeros of p-adic L-functions over non-abelian extensions. Glasgow Mathematical Journal, 58(02), 385-432. doi:10.1017/S0017089515000245 Open Access version: https://hdl.handle.net/10289/9749
Delbourgo, D., & Lei, A. (2016). Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction. Mathematical Proceedings of the Cambridge Philosophical Society, 160(1), 11-38. doi:10.1017/S0305004115000535