Postgraduate research topics in pure mathematics

Thinking of doing a PhD or research degree in pure mathematics? Here are some suggested topics.

Alternatively, you may have your own topic ideas you'd like to explore. In that case, talk to staff with related interests about developing a proposal.

Supervisor: Professor Xuan Duong

Topic Description:

In this project, the student will study some topics of modern harmonic analysis which aim to estimate different types of singular integrals on various function spaces. Some parts of this topic are related to the current research of harmonic analysis and partial differential equations.

Supervisor: Dr Ji Li

Topic Description:

The student will study some recent developments and topics in modern harmonic analysis, such as singular integrals and the related function spaces, (1) on domains arisen in the complex setting; (2) associated to differential operators arisen from partial differential equations.

Supervisor: Associate Professor Adam Sikora

Topic Description:

Research Project - Riesz transform for Grushin-type operators

Supervisor: Dr The Anh Bui

Topic Description:

One of the major themes of harmonic analysis is the study of singular integrals on certain function spaces which rely on the theory of Calderon-Zygmund operators. We emphasize that this theory plays an important role in analysis and has a strong influence on other branches of mathematics including the study of partial differential equations. However, in practice there are a number of important settings which do not fall within its scope.

The main aim of this project is to study the boundedness of singular integrals beyond the Calderon-Zygmund theory and applications in partial differential equations.