## Publications and preprints

#### Publications

*Refined Selmer equations for the thrice-punctured line in depth two*

(with A.J. Best, T. Kumpitsch, M. Lüdtke, A.W. McAndrew, L. Qian, E. Studnia and Y. Xu)

Math. Comp., to appear

arXiv:2106.10145*Local constancy of pro-unipotent Kummer maps*

Proc. Lond. Math. Soc.,**127**(3), pp836–888, 2023

doi:10.1112/plms.12554 | arXiv:2203.03701 | Erratum*Weight filtrations on Selmer schemes and the effective Chabauty–Kim method*

Compos. Math.,**159**(7) pp1531–1605, 2023

doi:10.1112/S0010437X2300725X | arXiv:2106.01218*The motivic anabelian geometry of local heights on abelian varieties*

Mem. Amer. Math. Soc., to appear

arXiv:1706.04850*Semisimplicity of the Frobenius action on π*_{1}

(with D. Litt)

in Proceedings of the Simons Symposium on*p*-adic Hodge Theory, Singular Varieties and Non-Abelian Aspects, pp17–64, 2023

doi:10.1007/978-3-031-21550-6 | arXiv:1912.02167*A user's guide to the local arithmetic of hyperelliptic curves*

(With A. Best, M. Bisatt, R. van Bommel, V. Dokchitser, O. Faraggi, S. Kunzweiler, A. Morgan, S. Muselli and S. Nowell)

Bull. Lond. Math. Soc.,**54**(3), pp825–867, 2022

doi:10.1112/blms.12604 | arXiv:2007.01749*Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction*

J. Number Theory**231**, pp158–213, 2022

doi:10.1016/j.jnt.2020.09.021 | arXiv:1808.05479*Variation of Tamagawa numbers of semistable abelian varieties in field extensions*

(with V. Dokchitser and A. Morgan)

Math. Proc. Cam. Phil. Soc.,**116**, pp487–521, 2019

doi:10.1017/S0305004118000075 | arXiv:1405.3151

#### Preprints

*Local heights on hyperelliptic curves and quadratic Chabauty*

(with J. Duque-Rosero, S. Hashimoto and P. Spelier)

arXiv:2401.05228*Chabauty–Kim and the Section Conjecture for locally geometric sections*

(with T. Kumpitsch and M. Lüdtke)

arXiv:2305.09462*Towards Uniform Chabauty–Kim*

(with D. Corwin and M. Leonhardt)

arXiv:2206.11085*Galois sections and p-adic period mappings*

(with J. Stix)

arXiv:2204.13674*The local theory of unipotent Kummer maps and refined Selmer schemes*

(with N. Dogra)

arXiv:1909.05734

#### Selected Talks

*Chabauty–Kim and the Section Conjecture for locally geometric sections*

Rational Points Workshop, Schney, 2023

Slides*Computing Local Heights for Quadratic Chabauty*

Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting*A partial finiteness theorem for the Selmer section set*

ADDING Conference, Athens GA, 2022*Weights of Coleman functions and effective Chabauty–Kim*

Workshop on Rational Points and Galois Representations, Pittsburgh (online), 2021*Galois sections and the Lawrence–Venkatesh method*

Queen Mary University Online Number Theory Seminar, 2020

Video | Slides*Weight filtrations on Selmer schemes and effective non-abelian Chabauty*

Online 'Selminar' on Selmer Schemes, 2020

Video | Slides*The Chabauty–Kim method*

Three-lecture mini-course at Paris 6, 2018*Iterated integrals, Green's functions and fundamental groups*

Bristol Linfoot Number Theory Seminar, 2017*Computing Tamagawa numbers of hyperelliptic curves*

ICTP Workshop on Hyperelliptic Curves, 2017

Slides*Local heights on abelian varieties via non-abelian Bloch–Kato Selmer sets*

BIRS Workshop on Nilpotent Fundamental Groups, 2017

Video*Non-abelian Bloch–Kato Selmer sets and an application to heights on abelian varieties*

3rd Workshop on Interactions between Homotopy and Arithmetic, 2017

Slides | Handout