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Algorithmic randomness and Fourier series
Johanna Franklin, Hofstra
Location: Hill 705
Date & time: Monday, 11 February 2019 at 5:00PM - 6:00PM
Abstract: A point in a probability space is called algorithmically random if it has no rare measure-theoretic properties that are simple to define via computability theory; the set of all such points will have measure 1 for any reasonable definition of randomness. Carleson's Theorem states that the Fourier series of certain integrable functions converge on a set of measure 1 as well. I will consider this theorem in the context of computable analysis and show that the points that satisfy this version of Carleson's Theorem are precisely the Schnorr random points.