05/24: Amir Algom

Abstract: A real number is called p-normal if its orbit under the (times p) map equidistributes for the Lebesgue measure. It is a fundamental problem, motivated by Borel’s normal number Theorem, to study which singular measures are supported on normal numbers. In this talk we will survey the classical approach of Davenport-Erdos-LeVeque, and the recent innovative approach of Hochman-Shmerkin. We will then introduce a new dynamical method to attack this problem for self-conformal measures, that also allows us to estimate their Fourier transform.

Joint work with Federico Rodriguez Hertz and Zhiren Wang.