# Simon Baker: Normal numbers and self-similar measures

**Time: **
Thu 2022-12-08 11.00

**Location: **
Room 3721, Lindstedtsvägen 25

**Participating: **
Simon Baker (Loughborough University)

**Abstract:** A real number x is said to be normal in base b if the sequence (b^n x) is uniformly distributed modulo one. In this talk I will discuss a recent result which states that for a self-similar measure and an integer b, if the self-similar measure and b satisfy a suitable arithmetic assumption, then almost every x is normal in base b with respect to the self-similar measure. This is a joint work with Amir Algom and Pablo Shmerkin.