OCT 19, 4:00 pm. / via Zoom

**Tom Cuchta**
*
Assistant Professor of Mathematics*

Fairmont State University

Fairmont State University

**
A strange Real Number
**

The goal of this talk is to show how the tools of ergodic theory can be used to show the existence of a real number with a surprising property. Ergodic theory is a branch of mathematics concerned with certain statistics related to deterministic systems. For example, consider the rotation map: if \theta is a fixed irrational angle and C is the circle formed by connecting the endpoints of [0,1], then the mapping T: C->C defined by T(x)=x+\theta is an "ergodic transformation". We will discuss the basic definitions of ergodic theory and talk briefly about the famous "ergodic theorem" which will be crucial to the goal of the talk.