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  6. GAnG - Prof Juan Valiente-Kroon

GAnG - Prof Juan Valiente-Kroon

Global problems in General Relativity: conformal methods and microlocal analysis

Supervisor: Professor Juan Valiente-Kroon

Project description:

The objective of this project is the development of techniques that bring together ideas from conformal geometry and microlocal analysis to study global evolution problems for the Einstein field equations. The development of these ideas is motivated by current developments in mathematical General Relativity and the desire to understand generic features of the evolution processes described by the Einstein field equations. 

The ideas of conformal geometry first introduced by Penrose have been deeply influential and have provided a way of reformulating global evolution problems as a finite existence time problems on manifolds with boundaries. The methods of Melrose’s School of microlocal analysis (the so-called geometric scattering theory) provides a convenient toolkit for the analysis of evolution problems on manifolds with boundary. A systematic approach to combing ideas from conformal scattering in Pernose’s framework has not yet been developed. This PhD project aims at developing such theory. Natural applications of these methods are to: 

  • The theory of asymptotic systems in General Relativity. 
  • The evolution of Cosmological spacetimes. 
  • The analysis of the nonlinear stability of black holes in both the asymptotically flat and cosmological setting. 

The present project is aimed at students with a solid background in Relativity and geometry who are interested in analytic methods of the theory of partial differential equations. It offers enough flexibility for tailoring the project according to their particular interests and abilities. Substantial parts of the project require the use of computer algebra methods. 

Basic references: 

  • J.A Valiente Kroon. Conformal methods in General Relativity. Cambridge University Press 2016. 
  • Richard B. Melrose. Geometric scattering theory. Cambridge Press 1995. 

Funding Notes:

This project is open to candidates applying for CSC/EPSRC/Underrepresented Studentships.

Further information: 
How to apply 
Entry requirements 
Fees and funding

PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/

 

As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award, we offer family-friendly benefits and support part-time study.  

 

 

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