Title: | Ergodic Theory and Normal Numbers. |

Speaker: | Drew D. Ash Adjunct Assistant Professor Mathematics and Computer Science Albion College Albion, Michigan |

Abstract: | The purpose of this talk is to expose the audience to subfield of dynamical system called ergodic theory. To do so, we will consider the following question. How many numbers in $[0,1)$ are there when we look at their base-10 decimal expansion have the following property: The asymptotic (or expected) frequency of seeing the digit $d$, $d\in\{0,1,\dots,9\}$, is $1/10$? Can you even think of a number that has this property? We will show, using ergodic theory, that a surprising amount of numbers have this property! If time allows, we will discuss another interesting transformation called the Gauss map. The Gauss map has connections with continued fractions! |

Location: | Palenske 227 |

Date: | 9/7/2017 |

Time: | 3:30 PM |

@abstract{MCS:Colloquium:DrewDAsh:2017:9:7, author = "{Drew D. Ash}", title = "{Ergodic Theory and Normal Numbers.}", address = "{Albion College Mathematics and Computer Science Colloquium}", month = "{7 September}", year = "{2017}" }