Slides from talks.

• Nonisomorphic curves that become isomorphic over extensions of coprime degrees, based on work with Danny Goldstein, Bob Guralnick, and Mike Zieve. Presented at the AMS/MAA joint meetings in San Diego, California in January 2008.
• Characteristic polynomials of automorphisms of hyperelliptic curves, based on an early version of this paper with Bob Guralnick. Note that the results improved after the talk was given. Presented at Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT-11), Centre International de Rencontres Mathématiques, Marseille, France, 5–9 November 2007.
• Even sharper upper bounds on the number of points on curves, based on work in progress with Kristin Lauter and on this paper. Presented at the first Symposium on Algebraic Geometry and its Applications, Papeete, French Polynesia, 7–11 May 2007, and at the University of California, San Diego number theory seminar, 24 May 2007.
• Higher-order Carmichael numbers, based on this paper. Colorado State University Mathematics Colloquium, 6 December 2006.
• Low-genus curves over finite fields: Problems and variations. Presented at the IPAM workshop on Open Problems in Number Theory and Cryptography, 9–13 October 2006.
• Jacobians in isogeny classes of abelian surfaces over finite fields, based on work with Enric Nart and Christophe Ritzenthaler. Presented at the AMS sectional meeting in San Francisco, California in April 2006. The TeX file for these slides is available as a sample of how to use Beamer with many of the features turned off.
• Pointless curves of genus three and four, based on work with Kristin Lauter and Jaap Top. Presented at the AMS/MAA joint meetings in San Antonio, Texas in January 2006.

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