Abel's Version of Abel's Theorem, Slides of a talk given at the Joint Mathematics Meetings, Baltimore, January 17, 2014

Galois's Version of Galois Theory, Galois Bicentennial Conference, Institut Henri Poincare, Paris, October 24, 2011, both streaming video and text of talk (under "videos" and "supports" respectively)

Style and Rigor in Mathematics, Oberwolfach Meeting on Disciplines and Styles in Pure Mathematics, March 1, 2010

Kronecker's Lost Theorem: An Insight into the Solvability of Algebraic Equations that Goes Beyond Galois, Streaming video of a talk given to the Pohle Colloquium, Adelphi University, November 5, 2008

Kronecker's Algorithmic Mathematics, Talk given at the conference "Computability in Europe 2008", Athens, Greece, June 19, 2008

The Algorithmic Side of Riemann's Mathematics, Talk given at the Joint Meetings of the AMS and MAA, San Diego, January 8, 2008

What Were Thought To Be the Foundations of Mathematics Before 1850?, Talk given at regional meetings of the AMS, Miami, FL, April 1, 2006

Summaries of two talks given at a Dagstuhl conference "Mathematics, Algorithms, Proofs" in January, 2005: 
Abel and the Concept of the Genus of a Curve
Introduction to My Book "Essays in Constructive Mathematics"

The Fundamental Theorem of Algebra from a Constructive Point of View, Slides of a talk given at Carnegie-Mellon University, April 15, 2004

The Use of Infinity in Mathematics, Talk given at St. John's College, Annapolis, MD, November 12, 2004