Research-Optimal properties of real numbers and their digit expansions

Research

Colloquium

Optimal properties of real numbers and their digit expansions

Speaker: Oliver Jenkinson（Queen Mary University of London）
Time: Sep 14, 2023, 14:00-15:00
Location: M1001, College of Science Building

Abstract:

Every rational number has a periodic (or eventually periodic) decimal digit expansion,

and this can be associated with a periodic orbit for the mapping x -> 10x (mod 1).

Fixing the arithmetic mean of such an orbit, or equivalently fixing the mean value of the digits in the decimal expansion,

we shall explore questions such as:

Which numbers give smallest variance around the mean?

Which numbers give largest geometric mean?

Brief profile/biography:

Oliver Jenkinson is Professor of Mathematics at Queen Mary, University of London, having worked there since 2000.

He works in ergodic theory and dynamical systems, with particular focus on ergodic optimization and thermodynamic formalism, and applications to other areas.