# Jiun-Chau Wang

## Noncommutative Probability And Boole's Transformation

Date Friday, April 1, 2016

The year 2015 marks the bicentenary of George Boole (1815-64), a largely self-taught math genius. Aside from his legendary work in mathematical logic, Boole proved in 1857 a surprising formula that shows the map $T(x)=x-1/x$ (Boole's transformation) preserves the Lebesgue measure on the real line. However, it will take another one hundred years for Adler and Weiss to show the ergodicity of this map.

We will discuss a noncommutative probability approach to this infinite ergodic theory of the Boole's transformation, and the main result is a sufficient condition for the recurrence and ergodicity of Boole type transformations on the real line.