Abbreviations

For more information about the lecture halls and seminar rooms, see our lecture room page. The names listed under "Technical Assistance" are student volunteers who will act as a contact person for technical questions of the lecturers and workshop speakers during the course or workshop.

Randomness in logic

The course aims to give a thorough introduction to effective randomness, a currently very active field of research in mathematical logic and theoretical computer science with still many open questions. It is possible to introduce students to the main lines of research in a rather short time. The five lecture course will cover: 1.) three approaches to effective randomness: game theoretic (martingales), measure theoretic (Martin-Loef tests), information theoretic (incompressibility, Kolmogorov complexity). 2.) properties of random sequences, extracting information from random sequences, Chaitin's Omega number. 3.) randomness for arbitrary distributions, Bernoulli measures, Hausdorff measures and dimension, randomness and fractal geometry. 4.) Stronger and weaker notions of randomness, randomness and computational complexity, arithmetical randomness, projective randomness, Solovay random reals. 5.) Randomness and determinacy, connections with the higher infinite. Prerequisites: Basic knowledge in Computability Theory (Turing machines, computably enumerable sets) and Mathematical Logic (basic set theory)