Patrick Ingram

This is roughly what I look like (photo by Elissa Ross)

Patrick Ingram


Research Assistant Professor
University of Waterloo

























To e-mail me, type pingram and then @ and then math.uwaterloo.ca

Just in case anyone's looking for it, here's my curriculum vitae.

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.

Some Publications (in print/accepted/submitted)

  1. P. Ingram, Cubic polynomials with periodic cycles of a specified multiplier, submitted.
  2. P. Ingram, Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group, submitted.
  3. B. Hutz and P. Ingram, Numerical Evidence for a Conjecture of Poonen, submitted.
  4. X. W. C. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes, T. J. Tucker, and M. E. Zieve, Uniform bounds on pre-images under quadratic dynamical systems, Mathematical Research Letters 16 number 1 (2009), pp. 87-101.
  5. P. Ingram, A quantitative primitive divisor result for elliptic divisibility sequences, to appear in Journal de Théorie des Nombres de Bordeaux.
  6. G. Everest, P. Ingram, and S. Stevens, Primitive divisors on twists of the Fermat cubic, to appear in LMS Journal of Computation and Mathematics.
  7. P. Ingram, Multiples of integral points on elliptic curves, Journal of Number Theory 129 issue 1 (2009), pp. 182-208.
  8. G. Everest, V. Mahé, P. Ingram, and S. Stevens, The uniform primality conjecture for elliptic curves, Acta Arithmetica, 134 (2008), pp. 157-181.
  9. P. Ingram, Lower bounds on the canonical height associated to the morphism \phi(z)= z^d+c, to appear in Monatshefte für Mathematik.
  10. P. Ingram and J. H. Silverman, Primitive divisors in arithmetic dynamics, Mathematical Proceedings of the Cambridge Philosophical Society 146 issue 2 (2009), pp. 289-302.
  11. P. Ingram and J. H. Silverman, Uniform estimates for primitive divisors in elliptic divisibility sequences, to appear in a forthcoming memorial volume for Serge Lang, published by Springer-Verlag.
  12. P. Ingram, Approximating algebraic numbers by j-invariants of elliptic curves, Acta Arithmetica 131 (2008), pp. 57-68.
  13. P. Ingram, Elliptic divisibility sequences over certain curves, Journal of Number Theory 123 issue 2 (2007), pp. 473-486.
  14. P. Ingram, Diophantine analysis and torsion on elliptic curves, Proceedings of the London Mathematical Society 94 no. 1 (2007), pp. 137-154.
  15. P. Ingram, On k-th power numerical centres, Comptes rendus mathematiques de l'Academie des sciences (2006).
  16. M. A. Bennett and P. Ingram, Torsion subgroups of elliptic curves in short Weierstrass form, Transactions of the American Mathematical Society 357 no. 8 (2005), pp. 3325-3337.

Teaching

I'm currently teaching Math 115 (Linear Algebra for Engineering), and all information for this course is being posted in UW-ACE. Next term I will be teaching PMATH 441/641 (Algebraic Number Theory).

Seminar

Timothy Caley and I are running a learning seminar out of Silerman's "Arithmetic of Elliptic Curves" this term, meeting Tuesdays at 11am.