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]

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!