For more information about this meeting, contact Stephen Simpson, Jan Reimann.
|Title:||A survey of partial randomness.|
|Speaker:||Stephen G. Simpson, Pennsylvania State University|
|A remarkable recent development in the foundations of mathematics is the concept of algorithmic randomness which was pioneered by Martin-L"of (1966), Schnorr (1971) and Kucera (1985) and developed over the past 15 years by many authors. Among the most fruitful generalizations of Martin-L"of's concept are various partial randomness notions which were pioneered by Reimann (2004) and other authors, with close connections to Hausdorff dimension, Kolmogorov complexity, and topological entropy. In this talk we shall survey several partial randomness notions and their uses. Among the notions considered are autocomplexity, non-K-triviality, and f-randomness where f is an arbitrary computable function from finite sequences of 0's and 1's to real numbers. As time permits we shall discuss results from the recent paper "Propagation of partial randomness" by Higuchi, Hudelson, Simpson and Yokoyama. The paper is available on-line as http://www.math.psu.edu/simpson/papers/ppr.pdf .|
Room Reservation Information
|Date:||09 / 04 / 2012|
|Time:||02:30pm - 03:45pm|