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Department of Pure Mathematics and Mathematical Statistics

 

Research Interests: PDE analysis, in particular hyperbolic PDE. Classical general relativity.

I am interested in partial differential equations (PDE), with particular application to problems arising in general relativity. PDE are equations that describe how a certain quantity varies from place to place. For example, the wave equation describes how the pressure of the air in a room changes as a function of space and time as a sound wave passes through it. The study of such equations is central to many areas of modern mathematics and physics. The class of PDE that I mostly study arise from the study of general relativity. General relativity is Einstein's theory of the gravitational field in which it is postulated that space and time together form a dynamical geometry, which evolves in time according to a PDE whose character is similar to that of the wave equation. In particular, solutions exists describing propagating gravitational waves, a fact that was recently given spectacular experimental corroboration by the results of LIGO in September 2015.

I'm a University Lecturer with a joint appointment between the two departments of the Faculty of Mathematics: the Department for Pure Mathematics and Mathematical Statistics (DPMMS) and the Department of Applied Mathematics and Theoretical Physics (DAMTP).

 

Publications

Helical phase of chiral nematic liquid crystals as the Bianchi VII group manifold
GW Gibbons, CM Warnick
– Phys Rev E Stat Nonlin Soft Matter Phys
(2011)
84,
031709
Optical metrics and projective equivalence
S Casey, M Dunajski, G Gibbons, C Warnick
– Physical Review D - Particles, Fields, Gravitation and Cosmology
(2011)
83,
084047
Some spacetimes with higher rank Killing-Stäckel tensors
GW Gibbons, T Houri, D Kubiznak, CM Warnick
– Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
(2011)
700,
68
Nonexistence of Skyrmion–Skyrmion and Skyrmion–anti-Skyrmion static equilibria
GW Gibbons, CM Warnick, WW Wong
– Journal of Mathematical Physics
(2011)
52,
012905
The geometry of sound rays in a wind
GW Gibbons, CM Warnick
– Contemporary Physics
(2011)
52,
197
Symmetries of the Dirac operator with skew-symmetric torsion
T Houri, D Kubiznak, C Warnick, Y Yasui
– Classical and Quantum Gravity
(2010)
27,
185019
Hidden symmetry in the presence of fluxes
D Kubiznak, CM Warnick, P Krtous
– Nuclear Physics B
(2011)
844,
185
Generalized hidden symmetries and the Kerr-Sen black hole
T Houri, D Kubiznak, CM Warnick, Y Yasui
– Journal of High Energy Physics
(2010)
2010,
55
Dark energy and projective symmetry
GW Gibbons, CM Warnick
– Physics Letters B
(2010)
688,
337
Traffic noise and the hyperbolic plane
GW Gibbons, CM Warnick
– Annals of Physics
(2010)
325,
909
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