**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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