Jan Vonk

Mathematical Institute, University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford, OX2 6GG (UK)

Office : N2.05
Phone : +44 1865 273553 (Office)
E-mail: vonk [-at-] maths [dot] ox [dot] ac [dot] uk


I am a postdoctoral research fellow in the group of Francis Brown, and a Junior Research Fellow at Linacre College.
CV

Bokrijk
Picture by Leo Vonk      

Publications

H. Darmon, J. Vonk
Ring class fields of real quadratic fields and cuspidal values of rigid meromorphic cocycles
Preprint (2018) (pdf)

J. Balakrishnan, N. Dogra, S. Müller, J. Tuitman, J. Vonk
Explicit Chabauty-Kim for the non-split Cartan modular curve of level 13
Annals of Math. (2) Volume 189, no. 3 (2019) (pdf)

H. Darmon, J. Vonk
Singular moduli for real quadratic fields: A rigid analytic approach
Preprint (2017) (pdf)

J. Vonk
Modular eigenforms at the boundary of weight space
Research in Number Theory 4:23 (2018) (pdf | journal)

J. Vonk
Crystalline cohomology of towers of curves
Int. Math. Res. Not. (IMRN) (pdf | journal)

J. Vonk
Computing overconvergent forms for small primes
LMS J. Comp. Volume 18, Issue 1 (2015), 250-257 (pdf | journal)

R. Möller, J. Vonk
Normal subgroups of groups acting on trees and automorphism groups of graphs
Journal of Group Theory, Volume 15, Issue 6 (2012), 831-850 (pdf | journal)


Teaching

Math 140 : Calculus I
McGill University, Winter 2016
(Course outline)

Math 235 : Algebra I
McGill University, Fall 2016
(Course outline)

Math 596 : Topics in Algebra and Number Theory
McGill University, Winter 2017
The course webpage and lecture notes are here.

Math 251 : Honours Linear Algebra
McGill University, Fall 2017
(Course outline)


Seminars and notes

Rational points on curves: A p-adic and computational perspective.
Oxford, 24 - 29 September (2012)
I co-organised (with Henri Darmon, Minhyong Kim and Alan Lauder) a conference, funded by the ERC.
The conference website can be found here, with notes from all the talks. A picture of (most) participants.

Deformation week
Oxford, 16 - 19 April (2013)
I co-organised (with Emily Cliff and Kristian Strømmen) a workshop, funded by the Mathematical Institute in Oxford.
The webpage is here.

Perverse sheaves and the decomposition theorem
Oxford, Michaelmas 2014
Balázs Szendrői and I ran a perversity seminar, the webpage can be found here.

Jacquet-Langlands and cyclic base change
Oxford, Michaelmas 2014
Minhyong Kim, Andrew Wiles, and I ran an automorphic seminar, the webpage can be found here.

Crystalline cohomology of towers of curves
Harvard, 12 April 2017
Slides from a talk given at the Harvard Number Theory Seminar.

Rigid meromorphic cocycles
Barcelona, June 2017
Notes from a series of lectures on joint work with Henri Darmon.

The Gross-Zagier formula
Oxford, Michaelmas 2018
Netan Dogra and I are running a seminar on Gross-Zagier, the webpage can be found here.


Code

Rigid meromorphic cocycles
Last updated: 1 August 2018
Henri Darmon and I wrote a Magma package to compute spaces of rigid meromorphic cocycles, as introduced in our paper 'Singular moduli for real quadratic fields'. It computes the following objects:
1) Rigid meromorphic cocycles attached to an RM point.
2) Their cuspidal values.
3) Their RM values.
4) Stark-Heegner points on elliptic curves, coming from to their parabolic lifting obstructions.
The code, and some instructions, may be found here.

Overconvergent modular forms
Last updated: 14 April 2018
This code builds on the code of Alan Lauder. It has two main branches, which compute:
1) The computation of spaces of overconvergent modular forms at integer weights, for any prime p, as well as routines to compute eigenforms, projections, and Chow-Heegner points on elliptic curves.
2) The computation of spaces of overconvergent modular forms at the boundary of weight space.
The code, and some instructions, may be found here.