Additive combinatorics of infinite sets via ergodic theoretic approach. The proposed project will utilise innovative ergodic theoretic approaches to enable us to address important questions in Additiv

Description

Additive combinatorics of infinite sets via ergodic theoretic approach. The proposed project will utilise innovative ergodic theoretic approaches to enable us to address important questions in Additive Combinatorics (Number Theory) and Fractal Geometry. In particular, we will resolve long-standing inverse additive problems for infinite sets, discover sum-product phenomena in Number Theory, and find a plethora of finite configurations in fractal sets. We will also extend the structure theory of one of the most popular mathematical models of quasi-crystals to a more extensive class of groups. This project will make significant contributions to Additive Combinatorics and Ergodic Theory and will bring the Australian research in these fields to ever greater heights.. Scheme: Discovery Projects. Field: 0101 - Pure Mathematics. Lead: A/Prof Alexander Fish