Hamonic analysis and spaces of functions on manifolds. Harmonic analysis is at the frontiers of many branches of mathematics including partial differential equations (PDEs) and differential geometry.

Description

Hamonic analysis and spaces of functions on manifolds. Harmonic analysis is at the frontiers of many branches of mathematics including partial differential equations (PDEs) and differential geometry. Aim I of this project is to resolve an important conjecture in harmonic analysis on manifolds concerning boundedness of the prototypical operator, the Riesz transformations, on manifolds. Aim II is to study fractional powers of operators and their associated function spaces. Expected outcomes are solutions to the proposed long-standing problems, original ideas and techniques to solve further important problems in PDEs. Benefit includes expanding knowledge to mathematical sciences, training future mathematicians and mathematical foundation for experts in some important industries in Australia.. Scheme: Discovery Projects. Field: 4904 - Pure Mathematics. Lead: Prof Xuan Thinh Duong