Prof. Jonny Stephenson, Visiting Assistant Professor of Mathematics and Statistics, will give a talk in the department colloquium on Friday, December 8.

Colloquium meets at 3:30 p.m. in GEM 120.  All are welcome, whether you’re registered for colloquium or not.

Prof. Stephenson’s title and abstract are below.

Title:  Algorithmic Randomness and Complexity

Abstract:
If you toss a coin twenty times, you might be suspicious if you got twenty heads, since you expect approximately the same number of heads as tails. But what if you got HTHTHTHTHTHTHTHTHTHT? That has the same number of heads and tails, but still seems suspicious compared to some more disordered result like HTTHTHHTHTHHHTTHTTHH.

This introductory talk will focus on an algorithmic approach to these questions based around the intuitive idea that random objects typically do not contain patterns, and (as a consequence) cannot be accurately described in a brief way. These ideas extend nicely to infinite sequences of coin tosses, where there are three elegant and equivalent definitions of algorithmic randomness, which will be informally introduced.

If time permits, we will also discuss an application of the ideas to searching for clusters in data sets.