Jef Laga's homepage

Jef Laga


Welcome to my webpage! I am a Postdoctoral Research Associate at Princeton University.
Recently, I obtained my PhD at the University of Cambridge under the supervision of Jack Thorne.

I am interested in algebraic and arithmetic geometry, with a focus on arithmetic statistics of algebraic curves and abelian varieties.
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: jl0793(at)princeton(dot)edu

Preprints/Publications

  • 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.
    To appear in Mathematische Annalen. [journal] [arxiv]

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

    Teaching

    Fall 2022: MAT104 Calculus II

    Reading groups

  • 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