EPSRC DTP Studentship
Title: Fourier analysis on manifold with symmetries
Institution: University of Bath
Department of Mathematical Sciences
PhD Supervisor: Dr V Fischer
Co-Supervisor: Prof. A Dooley
Application Deadline: Thursday, October 29, 2015
Expected start date: January 2016.
Funding Availability: only to UK citizens or those who have been resident in the UK for a period of 3 years or more, see https://www.epsrc.ac.uk/skills/students/help/eligibility/
Project background: Symmetries appear all around us in the natural world, and therefore are ubiquitous in science. In mathematics, this has led to defining Lie groups (for example any group of real matrices) and homogeneous domains (for instance the sphere). The analysis in this context builds on studying Fourier series and Fourier transforms. It aims at understanding decompositions of functional spaces and operators using spectral methods and representation theory. Another aspect of Fourier and harmonic analysis is concerned with more Euclidean methods. From that area, in the 1960’s, a new branch emerged and became an independent theory, that of pseudo-differential operators and phase-space analysis.
Project overview: Phase-space analysis in the context of Lie groups is a natural and interesting question; this is the underlying theme of the proposal. This brings various aspects of analysis and partial differential equations together with algebra and geometry. Very recent inputs in this area are leading to revisiting old results with modern methods. Their potential applications in numerical analysis and probability are yet to be developed.
Supervisory team: The successful applicant will join the group of Dr Veronique Fischer who has recently moved to the University of Bath as a senior lecturer. She is an expert in phase-space analysis on Lie groups with a specialised book on the subject to be published in April 2016. She will provide detailed support for the student while Professor Anthony Dooley has complimentary expertise in harmonic analysis on Lie groups and will also participate in the supervisory team looking after the student.
The successful applicant will benefit from an EPSRC DTP studentship. This will cover their tuition fees (Home/EU rate), a training support fee of £1,000/annum and a stipend of approximately £14,057/annum (14/15 rate) for 3 and a half years.
For more information, contact Dr Veronique Fischer.
See also the advertisement on the website: