This page contains some of my mathematical research and code.

Publications

Here is a list of my mathematical publications.

• H. Darmon, J. Vonk
  p-Adic Green's functions for real quadratic geodesics
  Submitted (pdf)
  
  
• J. Vonk
  Rigid cocycles and singular moduli for real quadratic fields
  Submitted (pdf)
  
  
• J. Balakrishnan, N. Dogra, S. Müller, J. Tuitman, J. Vonk
  Quadratic Chabauty for modular curves
  Compositio Math., Vol. 159, No. 6 (2023), 1111-1152 (pdf | journal)
  
  
• H. Darmon, A. Pozzi, J. Vonk
  The values of the Dedekind-Rademacher cocycle at real multiplication points
  J. Eur. Math. Soc. (JEMS) Vol. 26, No. 10 (2024), 3987-4032 (pdf | journal)
  
  
• H. Darmon, J. Vonk
  Real quadratic Borcherds products
  Pure Appl. Math. Q. (Special Issue in honor of Dick Gross), Vol. 18, No. 5 (2022), 1803-1865 (pdf | journal)
  
  
• J. Vonk
  Overconvergent modular forms and their explicit arithmetic
  Bull. Amer. Math. Soc., Vol. 58, No. 3 (2021), 313-356 (pdf | journal)
  
  
• H. Darmon, J. Vonk
  Arithmetic intersections of modular geodesics
  J. Number Theory (Prime), Vol. 230 (2022), 89-111 (pdf | journal)
  
  
• A. Lauder, J. Vonk
  Computing p-adic L-functions of totally real fields
  Math. Comp., Vol. 91, No. 334 (2022), 921-942 (pdf | journal)
  
  
• H. Darmon, A. Pozzi, J. Vonk
  Diagonal restrictions of p-adic Eisenstein families
  Math. Ann., Vol. 379, No. 1 (2021), 503-548 (pdf | journal)
  
  
• J. Balakrishnan, A. Best, F. Bianchi, B. Lawrence, N. Triantafillou, S. Müller, J. Vonk
  Two recent p-adic approaches towards the (effective) Mordell conjecture
  "Arithmetic L-Functions and Differential Geometric Methods", Progress in Math., Vol. 338, 31-74, Birkhäuser (pdf | book)
  
  
• J. Balakrishnan, N. Dogra, S. Müller, J. Tuitman, J. Vonk
  Explicit Chabauty-Kim for the non-split Cartan modular curve of level 13
  Ann. of Math. (2) Vol. 189, No. 3 (2019), 885-944 (pdf | journal)
  
  
• H. Darmon, J. Vonk
  Singular moduli for real quadratic fields: A rigid analytic approach
  Duke Math. J., Vol. 170, No. 1 (2021), 23-93 (pdf | journal)
  
  
• J. Vonk
  Modular eigenforms at the boundary of weight space
  Res. Number Theory, Vol. 4, No. 2 (2018) (pdf | journal)
  
  
• J. Vonk
  Crystalline cohomology of towers of curves
  Int. Math. Res. Not. (IMRN), Vol. 2020, No. 21, 7454-7488 (pdf | journal)
  
  
• J. Vonk
  Computing overconvergent forms for small primes
  LMS J. Comp., Vol. 18, No. 1 (2015), 250-257 (pdf | journal)
  
  
• R. Möller, J. Vonk
  Normal subgroups of groups acting on trees and automorphism groups of graphs
  J. Group Theory, Vol. 15, No. 6 (2012), 831-850 (pdf | journal)
  
  

My publication profile on external databases:

• Google Scholar
• zbMath Open
• ORCID

Expository

Some expository mathematical notes for talks, mini-courses, etc.

• Rational points on modular curves
  
  ICTS Bangalore, September 2023
  
  Notes from a lecture series at the ICTS Summer School on rational points on modular curves. The focus of this course was on arithmetic properties of cusps and CM points, and to illustrate the works of Mazur and Gross-Zagier in an examples-based way.



• Torsion points on elliptic curves
  
  Hay-on-Wye, August 2022
  
  Notes from a mini-course at the CMI Graduate Summer School on elliptic curves, held at Baskerville Hall. The lectures were on the theme of torsion points on elliptic curve, and center around two foundational results: The theorem of Mazur on torsion of elliptic curves over Q, and the open image theorem of Serre.



• Rigid cocycles and singular moduli for real quadratic fields
  
  Park City Utah, August 2022
  
  Notes from a mini-course at the PCMI 2022 Graduate Summer School, held in Park City. The theme of the programme was Number Theory Informed by Computation, and these lectures focus on the computation of rigid cocycles, and how experiments played a role in the development of their theory.



• Topics in Number Theory: p-Adic L-functions
  
  Leiden, Spring 2021
  
  Notes for part of a master course at Leiden. The aim is to give a friendly introduction to the theory of p-adic measures and Mellin transforms, and how they are used to define the Kubota-Leopoldt p-adic zeta function. The approach borrows from the beautiful treatment by Pierre Colmez.



• Some spectral questions over R and Q_p
  
  IAS Princeton, Spring 2020
  
  Expanded notes that grew out of an experimental talk in the Séminaire Shimizu. Its aim was to give an introduction to the subject of p-adic modular forms, and explore experimentally a number of analogies with the spectral theory of the Laplacian on Maass forms suggested by Frank Calegari.



• Overconvergent modular forms and their explicit arithmetic
  
  Bordeaux, June 2019
  
  Notes from a mini-course at the Iwasawa 2019 summer school. The lectures were about the basic theory of overconvergent modular forms, and their explicit computation following the algorithm of Lauder. An expanded version of these notes was later published in the Bulletin of the AMS.



• Rigid meromorphic cocycles
  
  Barcelona, June 2017
  
  A rough set of notes from a series of lectures on joint work with Henri Darmon, given during the summer of 2017 at UPC Barcelona, as part of a seminar run by Víctor Rotger.
  
  

Code

Some code written as part of my mathematical research, also available on GitHub

• Rigid meromorphic cocycles
  
  Henri Darmon and I wrote a Magma package to compute spaces of rigid meromorphic cocycles, as introduced in our papers
  
  1. Singular moduli for real quadratic fields (Duke Math. J. 2021)
  2. Arithmetic intersections of modular geodesics (J. Number Theory 2022)
  3. Real quadratic Borcherds products (Pure Appl. Math. Q. 2022)
  It computes rigid meromorphic theta cocycles, their RM values, their cuspidal values, as well as Stark-Heegner points on elliptic curves.



• Overconvergent modular forms
  
  This code builds on the code of Alan Lauder, and some parts of it were also written jointly with him. It has three main branches, which compute:
  
  1. Spaces of overconvergent modular forms for any prime p, as well as routines to compute eigenforms, projections, and Chow-Heegner points on elliptic curves.
     Computing overconvergent forms for small primes (LMS J. Comp. 2015)
     
  2. Spaces of overconvergent modular forms at the boundary of weight space.
     Modular eigenforms at the boundary of weight space (Res. Number Theory 2018)
     
  3. p-Adic L-functions of totally real fields (with A. Lauder).
     Computing p-adic L-functions of totally real fields (Math. Comp. 2022)
  
  
  
• Quadratic Chabauty
  
  The following code, building crucially on code written by Jan Tuitman, is based on the following papers with Jennifer Balakrishnan, Netan Dogra, Steffen Müller, and Jan Tuitman
  
  1. Explicit Chabauty-Kim for the non-split Cartan modular curve of level 13 (Ann. Math. 2019)
  2. Quadratic Chabauty for modular curves (Compos. Math. 2023)