Patrick Ingram
Patrick Ingram

Patrick Ingram

Assistant 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 first by general topic, and then 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."

Arithmetic dynamics

  1. Critical orbits of polynomials with a periodic point of specified multiplier
    draft available on the arxiv
  2. The critical height is a moduli height
    draft available on the arXiv
  3. p-adic uniformization and the action of Galois on certain affine correspondences
    draft available on the arXiv
  4. Canonical heights and preperiodic points for weighted homogeneous families of polynomials
    draft available on the arXiv
  5. Finite ramification for preimage fields of postcritically finite morphisms
    draft available on the arXiv
  6. Critical dynamics of variable-separated affine correspondences
    draft available on the arXiv
  7. Canonical heights for correspondences
    draft available on the arXiv
  8. Rigidity and height bounds for certain post-critically finite endomorphisms of projective space
    draft available on the arXiv
  9. Variation of the canonical height for polynomials in several variables
    draft available on the arXiv
  10. 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
  11. Canonical heights for Hénon maps
    Proceedings of the London Mathematical Society, Volume 108 (2014), no. 3, pp. 780-808.
    draft available on the arXiv
  12. 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
  13. A finiteness result for post-critically finite polynomials
    International Mathematics Research Notices, issue 3 (2012), pp. 524-543.
    draft available on the arXiv
  14. 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
  15. 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
  16. 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
  17. Uniform bounds on pre-images under quadratic dynamical systems
    Mathematical Research Letters 16 number 1 (2009), pp. 87-101
    draft available on the arXiv
  18. Lower bounds on the canonical height associated to the morphism f(z) = z^d + c
    Monatshefte für Mathematik 157 (2009), pp. 69-89
    draft available on the arXiv
  19. Primitive divisors in arithmetic dynamics
    draft available on the arXiv

Drinfeld modules

  1. The torsion submodule of an abelian t-module
    in preparation
  2. The filled Julia set of a Drinfeld module and uniform bounds for torsion
    submitted, arXiv
  3. A lower bound for the canonical height associated to a Drinfeld module
    draft available on the arXiv

Elliptic curves and surfaces

  1. 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
  2. Multiples of integral points on elliptic curves
    Journal of Number Theory 129 issue 1 (2009), pp. 182-208
    draft available on the arXiv
  3. Approximating algebraic numbers by j-invariants of elliptic curves
    Acta Arithmetica 131 (2008), pp. 57-68
    draft available
  4. Diophantine analysis and torsion on elliptic curves
  5. Torsion subgroups of elliptic curves in short Weierstrass form

Algebraic divisibility sequences

  1. Algebraic divisibility sequences over function fields
    draft available on the arXiv
  2. A quantitative primitive divisor result for elliptic divisibility sequences
    Journal de Théorie des Nombres de Bordeaux 21 fascicule 3 (2009), pp. 609-634
  3. Primitive divisors on twists of the Fermat cubic
    with G. Everest and S. Stevens
    draft available on the arXiv
  4. 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
  5. Uniform estimates for primitive divisors in elliptic divisibility sequences
  6. 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

Solving diophantine equations

  1. On k-th power numerical centres
    Comptes rendus mathematiques de l'Academie des sciences (2006)
    a draft is available

Teaching

This fall (2017) I am teaching Algebraic Number Theory, MATH 6115 on MWF 12:30-13:20 (in different rooms on different days, unfortunately!).