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 JMM Special Session, Slides for 18 lectures at a Joint Math Meeting Special Session, 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)
• Taxicabs and Sums of Two Cubes, Current Version of a Talk for Undergraduates, March 2013. (Powerpoint)
• Canonical Heights, Nef Divisors, and Arithmetic Degrees, Conference on Diophantine Problems and Arithmetic Dynamics, Academia Sinica, Taipei, Taiwan, June 24--28, 2013
• Arithmetic Dynamics JMM Special Session, Slides for 20 lectures at a Joint Math Meeting Special Session Seattle, January 2016
• Moduli Spaces for Dynamical Systems, Plenary Lecture, CNTA Calgary, June 2016
• Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions, Simons Symposium on Algebraic, Complex and Arithmetic Dynamics, Schloss Elmau, Germany, May 2019
• Arithmetic Dynamics, Arithmetic Geometry, and Number Theory, MAGNTS: Midwest Arithmetic Geometry and Number Theory Symposium The Ohio State University, October 2019
• Arithmetic Dynamics JMM Special Session, Slides for 24 lectures at a Joint Math Meeting Special Session, Denver, January 2020