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

  • Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
    To appear in Journal of Number Theory
    arXiv preprint
  • 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 preprint

Preprints

  • 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)
    arXiv preprint
  • The local theory of unipotent Kummer maps and refined Selmer schemes
    (with N. Dogra)
    arXiv preprint
  • Semisimplicity and weight--monodromy for fundamental groups
    (with D. Litt)
    arXiv preprint
  • The motivic anabelian geometry of local heights on abelian varieties
    arXiv preprint

Selected Talks

  • 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)