Patrick Ingram
Patrick Ingram

Patrick Ingram

Assistant Professor
Colorado State University

To e-mail me, type pingram and then @ and then math.colostate.edu (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.

Drinfeld modules

  1. The filled Julia set of a Drinfeld module and uniform bounds for torsion
    submitted
  2. A lower bound for the canonical height associated to a Drinfeld module
    submitted

Arithmetic dynamics

  1. Critical orbits and attracting cycles in p-adic dynamics
    (with Rob Benedetto, Rafe Jones, and Alon Levy)
    submitted
  2. Canonical heights for Hénon maps
    to appear in Proceedings of the London Mathematical Society
  3. Arboreal Galois representations and uniformization of polynomial dynamics
    to appear in Bulletin of the London Mathematical Society
  4. A finiteness result for post-critically finite polynomials
    International Mathematics Research Notices, issue 3 (2012), pp. 524-543.
  5. Variation of the canonical height for a family of polynomials
    to appear in Journal fur die reine und angewandte Mathematik.
  6. Cubic polynomials with periodic cycles of a specified multiplier
    Canadian Journal of Mathematics, 64 no. 2 (2012), pp. 318-345 .
  7. Numerical Evidence for a Conjecture of Poonen
    (with B. Hutz)
    to appear in the Rocky Mountain Journal of Mathematics.
  8. Uniform bounds on pre-images under quadratic dynamical systems
    (with X. W. C. Faber, B. Hutz, R. Jones, M. Manes, T. J. Tucker, and M. E. Zieve)
    Mathematical Research Letters 16 number 1 (2009), pp. 87-101.
  9. Lower bounds on the canonical height associated to the morphism \phi(z)= z^d+c
    Monatshefte für Mathematik 157 (2009), pp. 69-89.
  10. Primitive divisors in arithmetic dynamics
    (with J. H. Silverman)
    Mathematical Proceedings of the Cambridge Philosophical Society 146 issue 2 (2009), pp. 289-302.

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.
  2. Multiples of integral points on elliptic curves
    Journal of Number Theory 129 issue 1 (2009), pp. 182-208.
  3. Approximating algebraic numbers by j-invariants of elliptic curves
    Acta Arithmetica 131 (2008), pp. 57-68.
  4. Diophantine analysis and torsion on elliptic curves
    Proceedings of the London Mathematical Society 94 no. 1 (2007), pp. 137-154.
  5. Torsion subgroups of elliptic curves in short Weierstrass form
    (with M. A. Bennett)
    Transactions of the American Mathematical Society 357 no. 8 (2005), pp. 3325-3337.

Algebraic divisibility sequences

  1. Algebraic divisibility sequences over function fields
    (with V. Mahé, J. H. Silverman, K. E. Stange, M. Streng)
    Journal of the Australian Mathematical Society 92 (2012), pp. 99-126.
  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)
    LMS Journal of Computation and Mathematics 12 (2009), pp. 54-81.
  4. The uniform primality conjecture for elliptic curves
    (with G. Everest, V. Mahé, and S. Stevens)
    Acta Arithmetica 134 (2008), pp. 157-181.
  5. Uniform estimates for primitive divisors in elliptic divisibility sequences
    (with J. H. Silverman)
    Number Theory, Analysis and Geometry Springer-Verlag, 2012.
  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.

Solving diophantine equations

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

Teaching

In the spring of 2012 I am teaching...