Patrick Ingram
Patrick Ingram

Patrick Ingram

Associate Professor
York University

To e-mail me, type pingram and then @ and then yorku.ca (unless you're a bot!)

Research

My research is in number theory, and in particular diophantine geometry. My specific interests lie in the arithmetic of elliptic curves and surfaces, and in the theory of dynamical systems over global fields.

Publications

These are listed in approximate reverse chronological order. Please note that draft versions on the arXiv may differ from published versions, and only the journal versions are "official."

  1. Solutions to difference equations have few defects
    draft available on the arxiv
  2. Effective finiteness of solutions to certain differential and difference equations
    draft available on the arxiv
  3. Degree gaps for multipliers and the dynamical Andre-Oort conjecture
    draft available on the arxiv
  4. Minimally critical regular endomorphisms of \(\mathbb{A}^N\)
    draft available on the arxiv
  5. Minimally critical endomorphisms of \(\mathbb{P}^N\)
    draft available on the arxiv
  6. Post-Critically Finite Maps on \(\mathbb{P}^n\) for \(n\geq 2\) are Sparse
    draft available on the arxiv
  7. Current Trends and Open Problems in Arithmetic Dynamics
    Bulletin (New Series) of the AMS, Volume 56, Number 4, October 2019, Pages 611–685, https://doi.org/10.1090/bull/1665, Published: 12 January 2018
    draft available on the arxiv
  8. Critical orbits of polynomials with a periodic point of specified multiplier
    draft available on the arxiv
    Math. Zeitschrift, 291, pp. 1245–1262 (2019)
  9. The critical height is a moduli height
    draft available on the arXiv
    Duke Math. J., Volume 167, Number 7 (2018), pp. 1311-1346.
  10. p-adic uniformization and the action of Galois on certain affine correspondences
    draft available on the arXiv
  11. Canonical heights and preperiodic points for weighted homogeneous families of polynomials
    draft available on the arXiv
  12. Finite ramification for preimage fields of postcritically finite morphisms
    draft available on the arXiv
    Math. Research Letters, Volume 24 (2017), Number 6
  13. Critical dynamics of variable-separated affine correspondences
    draft available on the arXiv
    J. London Math. Soc., Volume 95, Issue 3, June 2017, pp. 1011-1034
  14. Canonical heights for correspondences
    draft available on the arXiv
    Trans. Amer. Math. Soc., DOI: https://doi.org/10.1090/tran/7288, Published electronically: May 30, 2018
  15. Rigidity and height bounds for certain post-critically finite endomorphisms of projective space
    draft available on the arXiv
    Canadian Journal of Mathematics, Volume 68 (2016), pp. 625-654 (see also!)
  16. The torsion submodule of an abelian t-module
    in preparation
  17. Variation of the canonical height for polynomials in several variables
    draft available on the arXiv
    International Mathematics Research Notices, Vol. 2015, No. 24, pp. 13545-13562
  18. The filled Julia set of a Drinfeld module and uniform bounds for torsion
    submitted, arXiv
  19. A lower bound for the canonical height associated to a Drinfeld module
    draft available on the arXiv
  20. Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps
    Duke Mathematical Journal, Volume 163, Number 13 (2014), pp. 2325-2356.
    draft available on the arXiv
  21. Canonical heights for Hénon maps
    Proceedings of the London Mathematical Society, Volume 108 (2014), no. 3, pp. 780-808.
    draft available on the arXiv
  22. Algebraic divisibility sequences over function fields
    draft available on the arXiv
  23. Arboreal Galois representations and uniformization of polynomial dynamics
    Bulletin of the London Mathematical Society, Volume 45 (2013), no. 2, pp. 301-308.
    draft available on the arXiv
  24. A finiteness result for post-critically finite polynomials
    International Mathematics Research Notices, issue 3 (2012), pp. 524-543.
    draft available on the arXiv
  25. Variation of the canonical height for a family of polynomials
    Journal fur die reine und angewandte Mathematik, Volume 685 (2013), pp. 73-97.
    draft available on the arXiv
  26. Cubic polynomials with periodic cycles of a specified multiplier
    Canadian Journal of Mathematics, 64 no. 2 (2012), pp. 318-345
    draft available on the arXiv
  27. Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group
    Algebra and Number Theory 5 no. 4 (2011), pp. 465-493
    draft available on the arXiv
  28. On Poonen's conjecture concerning rational preperiodic points of quadratic maps
    with B. Hutz
    Rocky Mountain Journal of Mathematics, Volume 43, Number 1 (2013), pp. 193-204.
    draft available on the arXiv
  29. Uniform bounds on pre-images under quadratic dynamical systems
    Mathematical Research Letters 16 number 1 (2009), pp. 87-101
    draft available on the arXiv
  30. A quantitative primitive divisor result for elliptic divisibility sequences
    Journal de Théorie des Nombres de Bordeaux 21 fascicule 3 (2009), pp. 609-634
  31. Primitive divisors on twists of the Fermat cubic
    with G. Everest and S. Stevens
    draft available on the arXiv
  32. Multiples of integral points on elliptic curves
    Journal of Number Theory 129 issue 1 (2009), pp. 182-208
    draft available on the arXiv
  33. The uniform primality conjecture for elliptic curves
    with G. Everest, V. Mahé, and S. Stevens
    Acta Arithmetica 134 (2008), pp. 157-181
    draft available on the arXiv
  34. Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d + c\)
    Monatshefte für Mathematik 157 (2009), pp. 69-89
    draft available on the arXiv
  35. Primitive divisors in arithmetic dynamics
    draft available on the arXiv
  36. Uniform estimates for primitive divisors in elliptic divisibility sequences
  37. Approximating algebraic numbers by j-invariants of elliptic curves
    Acta Arithmetica 131 (2008), pp. 57-68
    draft available
  38. Elliptic divisibility sequences over certain curves
    Journal of Number Theory 123 issue 2 (2007), pp. 473-486
    Received one of twenty "Top Cited Article 2007 - 2011" awards from JNT
    a draft, fraught with errors, is available
  39. Diophantine analysis and torsion on elliptic curves
  40. On k-th power numerical centres
    Comptes rendus mathematiques de l'Academie des sciences (2006)
    a draft is available
  41. Torsion subgroups of elliptic curves in short Weierstrass form

Teaching

NOPE (2020-2021)