Tue, March 8, 2022
1:45 pm - 2:45 pm
066 University Hall
Title: Introduction to effective randomness
Speaker: Li Ling Ko (The Ohio State University)
Abstract: In this introductory talk, I will provide three notions of randomness of reals --- Martin-Lof randomness, Solovay randomness, and Levin-Chaitin randomness. These definitions are well studied in computability theory and are known to be equivalent. I will also introduce a fundamental tool in the study of randomness --- Van Lambalgen's theorem, which formalizes the intuition that two subsequences in a random real should be highly independent, and also conversely, that two sequences that are random relative to each other should join to a random real.