PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jason Rute, Stephen Simpson, Jan Reimann.

Title:Uniform distribution and algorithmic randomness
Seminar:Logic Seminar
Speaker:Jeremy Avigad, Carnegie Mellon University
Abstract:
A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct integers, then, for almost every real number x, the sequence (a_n x) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (a_n x) is uniformly distributed modulo one for every *computable* sequence (a_n) of distinct integers. Call such an x *UD random*. Every Schnorr random real is UD random, but there are Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random.

Room Reservation Information

Room Number:MB315
Date:10 / 21 / 2014
Time:02:30pm - 03:45pm