Colorado State University
To e-mail me, type pingram and then @ and then math.colostate.edu (unless you're a bot!)
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.
These are listed first by general topic, and then in approximate reverse chronological order.
The filled Julia set of a Drinfeld module and uniform bounds for torsion
A lower bound for the canonical height associated to a Drinfeld module
Critical orbits and attracting cycles in p-adic dynamics
(with Rob Benedetto, Rafe Jones, and Alon Levy)
Canonical heights for Hénon maps
to appear in Proceedings of the London Mathematical Society
Arboreal Galois representations and uniformization of polynomial dynamics
to appear in Bulletin of the London Mathematical Society
result for post-critically finite polynomials
International Mathematics Research Notices, issue 3 (2012), pp. 524-543.
Variation of the canonical height
for a family of polynomials
to appear in Journal fur die reine und angewandte Mathematik.
Cubic polynomials with periodic cycles of a
Canadian Journal of Mathematics, 64 no. 2 (2012), pp. 318-345 .
Numerical Evidence for
a Conjecture of Poonen
(with B. Hutz)
to appear in the Rocky Mountain Journal of Mathematics.
Uniform bounds on
under quadratic dynamical systems
(with X. W. C.
B. Hutz, R.
Jones, M. Manes, T.
J. Tucker, and M. E.
Mathematical Research Letters 16 number 1 (2009), pp.
Lower bounds on
canonical height associated to the morphism \phi(z)= z^d+c
Monatshefte für Mathematik 157 (2009), pp.
in arithmetic dynamics
(with J. H.
Mathematical Proceedings of
the Cambridge Philosophical Society 146 issue 2 (2009),
Elliptic curves and surfaces
Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group
Algebra and Number Theory 5 no. 4 (2011), pp. 465-493.
Journal of Number Theory 129 issue 1
(2009), pp. 182-208.
Approximating algebraic numbers by
j-invariants of elliptic curves
Arithmetica 131 (2008), pp. 57-68.
analysis and torsion on elliptic
Proceedings of the London Mathematical Society 94 no. 1
(2007), pp. 137-154.
Torsion subgroups of elliptic curves
in short Weierstrass form
(with M. A.
Transactions of the American
Society 357 no. 8 (2005), pp. 3325-3337.
Algebraic divisibility sequences
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.
A quantitative primitive divisor
Journal de Théorie des Nombres de
Bordeaux 21 fascicule 3 (2009), pp. 609-634.
twists of the Fermat cubic
and S. Stevens)
LMS Journal of Computation and Mathematics 12 (2009),
The uniform primality
conjecture for elliptic curves
and S. Stevens)
Acta Arithmetica 134 (2008), pp. 157-181.
Uniform estimates for primitive
divisors in elliptic divisibility
(with J. H.
Number Theory, Analysis and Geometry Springer-Verlag, 2012.
divisibility sequences over certain
Journal of Number Theory 123 issue 2 (2007),
Received one of twenty "Top Cited Article 2007 - 2011" awards from JNT.
Solving diophantine equations
- On k-th power numerical
mathematiques de l'Academie des sciences (2006).
In the spring of 2012 I am teaching...