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

Preprints/Publications

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]

Teaching

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]

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!