Professor in Number Theory
Research Interests: My research interests are in arithmetical algebraic geometry and computational number theory. In particular I work on elliptic curve descent calculations, and the construction of explicit elements in the Tate-Shafarevich group.
Publications
Computing structure constants for rings of finite rank from minimal free resolutions
– Mathematical Research Letters
(2024)
30,
1011
(doi: 10.4310/mrl.2023.v30.n4.a2)
Computing the Cassels-Tate pairing on the 2-Selmer group of a genus 2
Jacobian
(2023)
The density of integral quadratic forms having a $k$-dimensional totally
isotropic subspace
(2022)
On binary quartics and the Cassels–Tate pairing
– Research in Number Theory
(2022)
8,
74
(doi: 10.1007/s40993-022-00376-z)
On binary quartics and the Cassels–Tate pairing
– Research in Number Theory
(2022)
8,
74
(doi: 10.1007/s40993-022-00376-z)
The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$
– Proceedings of the London Mathematical Society
(2022)
124,
713
(doi: 10.1112/plms.12438)
Computing structure constants for rings of finite rank from minimal free
resolutions
(2021)
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