Lectures

These are slides from selected talks I given over the years at conferences and seminars. For a complete list of my talks please refer to my CV.

• A brief history of randomness [pdf]
   
• Turing degrees and randomness for continuous measures [pdf]
   
• Kolmogorov complexity and Diophantine approximation [pdf]
   
• Randomness and definability hierarchies [pdf]
   
• Effective aspects of diophantine approximation [pdf]
   
• Random graphs, finite extension constructions, and complexity [pdf]
   
• Algorithmic randomness and determinacy [pdf]
   
• Stochasticity for random graphs [pdf]
   
• The topology of random graphons [pdf]
   
• Patterns in Nature [pdf]
  Penn State Brandywine, Spring Speaker Series, April 2015 see also: http://brandywine.psu.edu/story/917/2015/04/02/explore-natures-geometry-nsf-researcher-april-8
   
• Algorithmically random point processes [pdf]
   
• Mini-Course on Algorithmic Randomness
  [Introduction] [Lecture 1] [Lecture 2] [Lecture 3] [Lecture 4] [Lecture 5]
  BASICS Summer School, Shanghai Jiao-Tong University, August 2014
   
• Effective multifractal spectra [pdf]
   
• Definability and Randomness [pdf]
   
• The Structure of NCR inside Δ_2 [pdf]
   
• Effective Geometric Measure Theory [pdf]
   
• Mutual Theories of Algorithmic Information [pdf]
   
• Measures and Their Random Reals [pdf]
   
• The Metamathematics of Randomness [pdf]
   
• Effectively Closed Set of Measures and Randomness [pdf]
   
• Randomness -- Beyond Lebesgue Measure [pdf]
   
• Effective Fractal Dimension [pdf]
   
• The Metamathematics of Algorithmic Randomness [pdf]
   
• Trees of Non-Trivial Hausdorff Measure in Computability Theory
   
• Fractal Dimensions in Recursion Theory [pdf]
   
• The Effective Dimension of Cones and Degrees [pdf]
   
• Measures and Randomness [pdf]
   
• Kolmogorov-Loveland Randomness and Stochasticity [pdf]
   
• On Hierarchies of Randomness Tests [pdf]
   
• Schnorr Dimension [pdf]
   
• Hausdorff Dimension, Randomness, and Entropy [pdf]
   
• Random Functions [pdf]
   
• Borel normaility, automata, and complexity [pdf]
   
• Hausdorff Dimension, Zufälligkeit und Berechenbarkeit [pdf]
   
• On Selection Functions that Do Not Preserve Normality [pdf]
   
• Hausdorff measures and perfect subsets [pdf]