Lectures

  1. Computability and Definability: Theory and Application, five lectures presented during the Introductory School on Definability, Decidability, and Computability, Hausdorff Research Institute for Mathematics, Bonn, Germany, September, 2025. [ videos ]
  2. Set Theoretic Aspects of Hausdorff Dimension, presented during Arctic Set Theory Workshop 7, Kilpisjärvi, Finland, February, 2025. [ pdf ]
  3. Effective Hausdorff Dimension and Applications, presented during the program Definability, Decidability, and Computability in Number Theory, Part 2, MSRI (now SLMath), Berkeley, CA, August, 2022. [ pdf ] [ video ]
  4. Computability Theory, Set Theory and Geometric Measure Theory, short course presented during Open Lectures for PhD Students in Computer Science, University of Warsaw, Poland, May, 2022. [ lectures, pdf ] [ exercises, pdf ]
  5. Three Theorems Between Computability and Diophantine Approximation, presented during Dagstuhl Workshop, February, 2017. [ pdf ]
  6. The Mathematics of Relative Definability, presented during the Joint Annual Meetings, Special AMS Session on Alan Turing, Boston, January, 2012. [ pdf ]
  7. Randomness and Recursion Theory, presented during Logic Colloquium 2010, Paris, France, July, 2010. [ 1, pdf ] [ 2, pdf ] [ 3, pdf ]
  8. Undecidability of the α-degrees, jointly with Chong Chi Tat, presented during the workshop Topics in Computability: A Meeting in Honor of Richard A. Shore, MIT, January, 2007. [ pdf ]
  9. Moduli of Computation, jointly with Marcia Groszek, presented during the Conference on Logic, Computability and Randomness, Buenos Aires, Argentina, January, 2007. [ pdf ]
  10. Effective Randomness for Continuous Measures, jointly with Jan Reimann, presented during the workshop Effective Randomness, American Institute of Mathematics, Palo Alto, California, August, 2006. [ pdf ]
  11. Turing Degrees and the Definability of the Turing Jump, presented to Computational Prospects of Infinity, Institute for Mathematical Sciences, Singapore, June 20 to August 15, 2005.
  12. Random Sequences and Recursive Measures, jointly with Jan Reimann, presented to CMS Winter Meeting, Special Session in Model Theory and Recursion Theory, Vancouver, Canada, December 7, 2003. [ pdf ]
  13. On Martin's Conjecture, presented to AMS Meeting, Special Session in Set Theory, Las Vegas, NV, April 21, 2001. [ pdf ]
  14. Recursion Theory, presented as The Gödel Lecture, Annual Meeting of the ASL, Philadelphia, PA, March 13, 2001. [ pdf ]