I work in the field of rational points on algebraic varieties. I am particularly interested in local-global principles in arithmetic geometry, and when and why such principles fail.

Publications and preprints

The texts available here may differ from the published versions.

• Machine learning for modular multiplication, joint with K. Lauter, C. Y. Li, K. Maughan and M. Srivastava (2024)  http://arxiv.org/abs/2402.19254

• Transcendental Brauer-Manin obstructions on singular K3 surfaces, joint with Mohamed Alaa Tawfik (2023). https://arxiv.org/abs/2311.00650

• Evaluating the wild Brauer group, joint with M. Bright.  Inventiones Mathematicae (2023). https://doi.org/10.1007/s00222-023-01210-8

• Distribution of genus numbers of abelian number fields, joint with C. Frei and D. Loughran. Journal of the London Mathematical Society, 107 (2023), 2197-2217. https://doi.org/10.1112/jlms.12737

• Explicit uniform bounds for Brauer groups of singular K3 surfaces, joint with F. Balestrieri and A. Johnson. Annales de l’Institut Fourier, 73 (2023), 567-607.

• Number fields with prescribed norms, joint with C. Frei and D. Loughran, with an appendix by Y. Harpaz and O. Wittenberg. Commentarii Mathematici Helvetici, 97 (2022), no. 1, 133–181.

• Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions, joint with A. Macedo. Mathematical Proceedings of the Cambridge Philosophical Society, 172(3) (2022), 489-529.

• The Hasse norm principle in global function fields, joint with A. Mânzăţeanu, E. Ozman, N. Sutherland and R. G. Uysal. Women in Numbers Europe III: Research Directions in Number Theory, Association for Women in Mathematics Series, vol 24, Springer (2021),  275-290.

• A bound on the primes of bad reduction for CM curves of genus 3, joint with P. Kılıçer, K. Lauter, E. Lorenzo García, E. Ozman and M. Streng. Proceedings of the American Mathematical Society, 148 (2020), 2843-2861.

• Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces, joint with Francesca Balestrieri. IMRN, rny303 (2019), https://doi.org/10.1093/imrn/rny303

• The Hasse norm principle for abelian extensions, joint with C. Frei and D. Loughran. Amer. J. Math 140(6) (2018), 1639-1685. Corrigendum.

• Non-ordinary curves with a Prym variety of low p-rank, joint with T. O. Celik, Y. Elias, B. Gunes, E. Ozman, R. Pries and L. Thomas. Women in Numbers Europe II. Association for Women in Mathematics Series, vol 11. Springer (2018), 117-158.

• Shadow lines in the arithmetic of elliptic curves, joint with J. Balakrishnan, M. Çiperiani, J. Lang and B. Mirza. Directions in Number Theory: Proceedings of the WIN3 Workshop, Springer (2016), 33-55.

• The proportion of failures of the Hasse norm principle, joint with T.D. Browning. Mathematika, 62, Issue 02, (2016), pp. 337–347.

• Strangely dual orbifold equivalence I, joint with Ana Ros Camacho, includes an appendix by Ana Ros Camacho and Federico Zerbini. Journal of Singularities 14 (2016).

• Transcendental Brauer groups of products of CM elliptic curves. J. London Math. Soc., 93 (2), (2016), 397–419. Corrigendum.

• Bad reduction of genus three curves with complex multiplication, joint with I. Bouw, J. Cooley, K. Lauter, E. Lorenzo Garcia, M. Manes and E. Ozman. Women in Numbers Europe, Research Directions in Number Theory, Association for Women in Mathematics Series Volume 2, Springer, DOI: 10.1007/978-3-319-17987-2

• Realising the cup product of local Tate duality, J. Théor. Nombres Bordeaux 27 (2015), 219 – 244.

• Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve, joint with T.A. Fisher, Int. J. Number Theory 10(2014), no. 7, 1881 – 1907.

• Explicit local reciprocity for tame extensions. Math. Proc. Camb. Philos. Soc. 152, Issue 03, April 2012, 425 – 454.

PhD thesis

Central simple algebras, cup-products and class field theory. University of Cambridge, 2012.