School Colloquium——When simple is best: Ergodic optimization, Sturmian orbits, and ergodic dominance
报告人：Oliver Jenkinson (Queen Mary, University of London)
For a given dynamical system, and a given real-valued function, the field of Ergodic Optimization seeks to understand those orbits (or invariant measures) that realise the largest possible ergodic average.
Rather often, these orbits turn out to be in some sense `simple', for example periodic, or non-periodic but of low complexity (e.g. Sturmian).
Ergodic dominance is one strategy, appealing to ideas from stochastic dominance, for understanding the optimizing orbits and measures for certain classes of functions.
One application is to constrained optimization problems for digit expansions: e.g. if we fix the mean value of the decimal digits of a number, or equivalently fix the arithmetic mean of an orbit under the map x-> 10x (mod 1), how can we minimize the variance around the mean, and how can we maximize the geometric mean?
Bio: 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. Prof. Jenkinson has published more than 40 papers on journals including Inventiones Mathematicae, Communications in Mathematical Physics, etc.