Pure Mathematics Topics

Pure Mathematics Topics

Topic Title: Singular integrals beyond Calderon-Zygmund theory and applications

Supervisor: Dr The Anh Bui

Topic Description:

One of the major themes of harmonic analysis is the study singular integrals on certain function spaces which rely on the theory of Calderon-Zygmund operators. We emphasize that the Calderon-Zygmund theory of singular integrals 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 the scope of the Calderon-Zygmund theory. 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.

Topic Title: Harmonic Analysis: estimates on singular integrals and function spaces

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.

Topic Title: Riesz transform for Grushin-type operators

Supervisor: A/Prof Adam Sikora

Topic Description:

Research  Project - Riesz transform for Grushin-type operators

Topic Title: Harmonic analysis and the applications to complex 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.

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