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

About me

Research interests

I am a postdoc at Harvard University, specialising in arithmetic and anabelian geometry. The main kinds of questions I'm interested involve relating fundamental groups of varieties to their arithmetic properties. For instance, my DPhil thesis, completed at the University of Oxford under the supervision of Minhyong Kim, showed that classical Néron--Tate height functions on abelian varieties admit very natural descriptions in terms of fundamental groups of Gm-torsors on abelian varieties.

Recent research highlights

  • With Netan Dogra, we proved a far-reaching generalisation of Oda's Criterion, asserting that the stable reduction type of a hyperbolic curve over a finite extension of Qp is determined by its pro-unipoten étale fundamental groupoid. As an application, we produced a refinement of the Chabauty--Kim method, allowing one to compute S-integral points on affine curves in cases where the usual Chabauty--Kim method fails.
  • With Daniel Litt, we proved several foundational properties of the Galois action on pro-unipotent étale fundamental groupoids, which are analogues of well-known properties of the first étale cohomology of varieties. This allowed us to study the geometry of non-abelian Bloch--Kato Selmer sets outside the case of good reduction, and can be viewed as a first step towards a ``Chabauty--Kim at primes of bad reduction''.

Outreach with UKMT

I also do a lot of volunteering for the United Kingdom Mathematics Trust, a charitable organisation providing mathematics enrichment for bright under-18s. As well as helping set and mark the British Mathematical Olympiads, I regularly teach at various summer schools and occasionally take teams of students abroad to international competitions.

You can find out more about the UKMT on their website, or the Olympiad subtrust website.