Alexander Betts
Postdoctoral Researcher in Mathematics

Contact details

Postal address:
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138

Email: abetts[at]math[dot]harvard[dot]edu

Publications and preprints

Publications

  • 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 π1
    (with D. Litt)
    in Proceedings of the Simons Symposium on p-adic Hodge Theory, Singular Varieties and Non-Abelian Aspects (to appear)
    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. (to appear)
    doi:10.1112/blms.12604
    arXiv:2007.01749
  • Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
    J. Number Theory 231(2022), pp158--213
    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(2019), pp487--521
    doi:10.1017/S0305004118000075
  • arXiv:1405.3151

Preprints

  • 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
  • Local constancy of pro-unipotent Kummer maps
  • arXiv:2203.03701
  • Weight filtrations on Selmer schemes and the effective Chabauty--Kim method
    arXiv:2106.01218
  • 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)
    arXiv:2106.10145
  • The local theory of unipotent Kummer maps and refined Selmer schemes
    (with N. Dogra)
    arXiv:1909.05734

Selected Talks

  • Grothendieck's section set and the Lawrence--Venkatesh method
    Connecticut Conference in Number Theory, 2022
  • A partial finiteness theorem for the Selmer section set
    ADDING Conference, Athens GA, 2022
  • Galois sections and the Lawrence--Venkatesh method
    Harvard Number Theory Seminar, 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
  • Weight--monodromy and canonical paths on varieties
    Paris 6&7 Number Theory Seminar, 2020
  • Non-abelian Kummer maps for curves
    Frankfurt Number Theory Seminar, 2019
  • 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

Other

  • Supplied proof of proposition 6.4. in On sets defining few ordinary lines by Ben Green and Terence Tao
  • Composed three problems used in the Romanian Master of Mathematics competitions (2011 Q5, 2013 Q2, 2015 Q3)