School of Mathematical Sciences

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Mr M J Cole

Michael Cole Queen Mary
Job title: 
Postgraduate Research Student
PhD Supervisor: 
Dr Juan Valiente-Kroon


I am a PhD student in the Geometry and Analysis Group in the School of Mathematical Sciences, at Queen Mary University of London. I am also a member of the Relativity and Cosmology group within the School of Physics and Astronomy.

My research interests relate to the mathematical analysis of Einstein's equations of general relativity and their solutions, in particular the global properties of spacetimes. I am investigating the construction of geometric invariants that measure the deviation of arbitrary solutions from interesting exact solutions, such as the Kerr solution (describing a rotating black hole). These invariants can be used to investigate various outstanding problems in general relativity such as the evolution of nonlinear perturbations of the Kerr solution, the uniqueness of black hole spacetimes, and the Penrose inequality.

Conferences and Workshops

99 Years of General Relativity; ESI-EMS-IAMP Summer school on Mathematical Relativity
Vienna, Austria, July 28th - August 1st, 2014
Junior scientist Andrejewski Days: 100 Years of General Relativity, Spring School
Brandenburg an der Havel, Germany, March 23rd - April 4th, 2015
The 15th British Gravity (BritGrav) Meeting
Birmingham, UK, 20 - 21st April 2015
Einstein's legacy: celebrating 100 years of general relativity
QMUL, London, 28th - 29th November 2015
6th Central European Relativity Seminar
Prague, Czech Republic, 28th - 30th January 2016
Collabor8; Meeting for early-career researchers
QMUL, London, 18th February 2016
GR21: 21st International Conference on General Relativity and Gravitation
New York, USA, 10th - 15th July 2016
Central European Relativity Seminar
Bremen, Germany, 16th - 18th February 2017


  • Semester 1, 2014/15 - Undergraduate mathematics tutorials: Essential Foundation Mathematics
  • Semester 2, 2014/15 - Undergraduate mathematics tutorials: Complex Variables, Differential Equations
  • Semester 3, 2014/15 - Undergraduate mathematics revision classes and drop-in sessions
  • Semester 1, 2015/16 - Undergraduate mathematics tutorials: Relativity
  • Semester 2, 2015/16 - Undergraduate mathematics tutorials: Calculus II
  • Semester 3, 2015/16 - Undergraduate mathematics revision classes and drop-in sessions
  • Semester 1, 2016/17 - Undergraduate mathematics tutorials: Relativity
  • Semester 2, 2016/17 - Undergraduate mathematics tutorials: Complex Variables
  • Semester 3, 2016/17 - Undergraduate mathematics revision classes and drop-in sessions

Grants and Prizes

  • Summer Undergraduate Research placement, University of Cambridge; Summer 2013
  • EPSRC Studentship in Perturbation Theory in Nonlinear Dynamical Systems (42 months). Start: September 2014
  • IOP Research Student Conference Fund; 2015
  • Ann Cook Poster Prize, 2nd Prize; May 2016
  • C R Barber Trust grant, July 2016


  • M. Cole & M. Dunajski, Twistor Theory of the Airy Equation, SIGMA 10 (2014), 037, arXiv:1401.0025
  • M. Cole & J. A. Valiente Kroon, Killing spinors as a characterisation of rotating black hole spacetimes, Class. Quantum Grav. 33, 125019 (2016), arXiv:1601.04666
  • M. Cole & J. A. Valiente Kroon, A geometric invariant characterising initial data for the Kerr-Newman spacetime, arXiv:1609.05129