Some mathematical notes I have written for talks, mini-courses, etc.

• 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 level course at the University of 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.