Antonín Kučera
(Charles University, Prague)
A Cornucopia of Randomness

We set out to give a general overview of notions of randomness - and, if time permits, ending on some more advanced topics. Main approaches to the study of randomness include those via Martin-Löf tests, martingales, and Kolmogorov complexity. There is, of course, a hierarchy of randomness, taking in Martin-Löf randomness, Schnorr randomness, Demuth randomness, and Oberwolfach randomness, amongst others. A particularly interesting and productive concept is that of K-triviality, and we will outline some of the more surprising and pleasing computability-theoretic properties of K-trivials.

The presentation will be kept approachable, assuming little more from the audience than a basic familiarity with relative Turing computability, or equivalent.