I am a Postdoctoral Research Associate at Princeton University.
In October I will start as a Research Fellow at St John's college, 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
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]
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!
