Selected Presentations (PDF and PowerPoint Slides)

The Ubiquity of Elliptic Curves: Version 1 and Version 2: (1) MAA Invited Lecture at JMM, Baltimore, January 2003; (2) Public Lecture, University College of Dublin, September 2007. (Powerpoint).
• A Number Theorist's Perspective on Dynamical Systems, Frontier Lectures, Texas A & M, April 2005 (PDF)
• An Introduction to Height Functions, Expanded version of lectures presented at MSRI, January 2006. (PDF)
• Summer School on Computational Number Theory and Applications to Cryptography, University of Wyoming, June/July 2006.
  • An Introduction to the Theory of Lattices (PDF),
  • An Introduction to the Theory of Elliptic Curves (PDF),
• Cambridge University, February, 2007.
  • The Arithmetic of Dynamical Systems, Kuwait Lecture. (PDF)
  • Independence of Heegner Points, Number Theory Seminar. (PDF)
• p-adic Properties of Elliptic Divisibility Sequences, Number Theory and Computability, ICMS Edinburgh, June 27, 2007. (PDF)
• The Four Faces of Lifting for the Elliptic Curve Discrete Logarithm Problem, 11th Workshop on Elliptic Curve Cryptography, University College Dublin, September 5, 2007. (PDF)
• Dynamics and Canonical Heights on K3 Surfaces with Noncommuting Involutions, Workshop on Rational Points on K3 Surfaces, BIRS, Banff, December 3, 2008. (PDF)
• Specialization Maps and Unlikely Intersections, Journees Arithmetique, St. Etienne, France July 6-10, 2009. (PDF)
• The Hitchhiker's Guide to Public Key Cryptography, Colloquium, Microsoft Research New England, December 2009. (Powerpoint)
• Arithmetic and p-adic Dynamics, Slides for 18 Special Session lectures at the Joint Math Meeting, San Francisco, January 2010
• Geometry and Arithmetic of Dominant Rational Self-Maps of Projective Space, Automorphisms of Algebraic Varieties — Dynamics and Arithmetic, Shirahama, Wakayama, Japan, December 19–23, 2011. (PDF)
• Joint Mathematics Meetings – Boston 2012
  • Number Theory and Dynamical Systems, MAA Invited Paper Session on the Beauty and Power of Number Theory (PDF)
  • Elliptic Pseudoprimes, AMS-SIAM Special Session on Mathematics of Computation: Algebra and Number Theory (PDF)
  • Number Theoretic Properties of Difference Equations Associated to Henon Maps, AMS Special Session on Global Dynamics of Rational Difference Equations with Applications (PDF)
  • Algebra, Geometry, and Dynamics of Pseudo-Real Maps, AMS Special Session on Dynamical Systems in Algebraic and Arithmetic Geometry (PDF)
  • Dynamical Cake (JPG)