# Department of Pure Mathematics and Mathematical Statistics

Professor (Grade 11) 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

On binary quartics and the Cassels-Tate pairing
T Fisher
– Research in Number Theory
(2022)
8,
74
The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$
M Bhargava, J Cremona, T Fisher, S Gajovic
– Proceedings of the London Mathematical Society
(2022)
124,
713
Everywhere local solubility for hypersurfaces in products of projective spaces
T Fisher, W Ho, J Park
– Research in Number Theory
(2021)
7,
6
The proportion of genus one curves over Q defined by a binary quartic that everywhere locally have a point
M Bhargava, J Cremona, T Fisher
– International Journal of Number Theory
(2020)
17,
903
Explicit moduli spaces for congruences of elliptic curves
T Fisher
– Mathematische Zeitschrift
(2019)
295,
1337
Some minimisation algorithms in arithmetic invariant theory
– Journal de Theorie des Nombres de Bordeaux
(2019)
30,
801
On some algebras associated to genus one curves
T Fisher
– Journal of Algebra
(2019)
518,
519
Visibility of 4-covers of elliptic curves
N Bruin, T Fisher
– Research in Number Theory
(2018)
4,
11
A formula for the Jacobian of a genus one curve of arbitrary degree
T Fisher
– Algebra and Number Theory
(2018)
12,
2123
Computing the Cassels–Tate pairing on 3-isogeny Selmer groups via cubic norm equations
M van Beek, T Fisher
– Acta Arithmetica
(2018)
185,
367
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E1.09

01223 764275