One of the core technical tools of harmonic analysis is to analyse functions by breaking them into simple building blocks.

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The Fourier transform is the most famous such decomposition. There the building blocks are the plane waves. However there are other analysis/synthesis systems, for example wavelets. 

 

In this project we use Fourier Integral Operators to develop analysis/synthesis systems that are well adapted (in the sense that the decomposition is sparse) to deal with wave equation like problems where there is some additional symmetry or dynamical constraints. 

 

I am currently advertising an available PhD scholarship to join my Marsden project 22-UOA-011 funded for this project. The scholarship covers all tuition fees for international and domestic students and includes a tax-free stipend of NZ$35,000 annually for up to three years.

• Applicants should have or expect to receive a BSc(Hons) or MSc or equivalent in mathematics. Candidates with strong analysis and PDE background are preferred.

• Applications including a CV, academic transcript, and cover letter should be sent to Dr. Melissa Tacy, melissa.tacy@auckland.ac.nz

• Applicants will need to also make a successful application for enrolment in doctoral study and the University of Auckland. You can find the full details of that application (including application deadlines) here

• Applications for the scholarship will be considered on a rolling basis until the position is filled, so apply soon to avoid disappointment!