Jef Laga's homepage

Jef Laga

Welcome to my webpage!

I am a Research Fellow at St John's College and a member of the number theory group at DPMMS, University of Cambridge.

I am interested in algebraic and arithmetic geometry.
More specifically, I enjoy thinking about the arithmetic of curves, abelian varieties and arithmetic statistics.
In my PhD thesis, I have shown how various results in arithmetic statistics can be unified and reproved using the theory of graded Lie algebras.

You can send me an email at: jcsl5(at)cam(dot)ac(dot)uk


  • Ceresa cycles of bielliptic Picard curves.
    Preprint, joint with Ari Shnidman. [arxiv]

  • Rational torsion points on abelian surfaces with quaternionic multiplication.
    Preprint, joint with Ciaran Schembri, Ari Shnidman and John Voight. [arxiv]

  • The geometry and arithmetic of bielliptic Picard curves.
    Preprint, joint with Ari Shnidman. [arxiv]

  • Graded Lie algebras, compactified Jacobians and arithmetic statistics.
    Preprint, based on my PhD thesis. [pdf] [arxiv]
    ([video] and [slides] from a talk about this work.)

  • Arithmetic statistics of Prym surfaces.
    Mathematische Annalen. [journal] [arxiv]

  • The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3.
    Algebra & Number Theory. [journal] [arxiv]


    Current: Examples classes for Part III Lie algebras. See the Moodle page for Example Sheets and more information.

    Spring 2023: MAT449 Representation theory. Here are the lecture notes in case they are useful: [lecture notes]

    Fall 2022: MAT104 Calculus II

    Reading groups

  • Fall 2022: Princeton Arithmetic Statistics learning seminar
  • Michaelmas 2021 (Arakelov intersection theory on Shimura Varieties): [schedule]
  • Lent-Easter 2021 (Automorphy lifting theorems): [schedule]
  • Michaelmas 2020 (Mazur's torsion paper): [schedule]
  • Lent-Easter 2020 (Weil II): following chapter I of this book
  • Michaelmas 2019 (Average ranks of elliptic curves): following this paper
  • Other notes

  • A note surveying some ADE classifications and connections between them, accompanying my talks ([video1] and [video2]) in Kazhdan's basic notions seminar: [pdf] (The second talk goes further than the note.)
  • A note defining the analytification functor in the rigid setting, together with the example of the Tate curve: [pdf]
  • Notes for a talk in this study group defining the etale homotopy type of a scheme with some examples: [pdf]
  • Statement of the Bloch-Kato conjecture on special values of L-functions: [pdf]
  • My Part III essay on Modular forms of weight one: [pdf]
  • A simple plane curve over the p-adics with bad reduction but whose Jacobian has good reduction:
  • Miscellaneous

  • Check out the Youtube channel Math-life balance, where Mura Yakerson interviews mathematicians in an interesting and personal way!
  • Bjorn Poonen has great advice on mathematical writing, speaking and being a PhD student
  • I strongly support Frederico Ardila's axioms
  • Check out Gender bias 101 for mathematicians