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Peter O'Donnell is a Fellow in Mathematics at Homerton College and a Fellow of the Institute of Mathematics. He also serves as Topical Editor in General Relativity and Gravitation for the journal Il Nuovo Cimento, and is Associate Editor of EPJ-Plus and a member of the editorial board of EJTP. Lecturing in Easter Term 2012 Mathematical Methods III, Part IA NST Details about his recent publications can be found here. Research interests include Lanczos potential theory, twistor theory, Non-linear partial differential equations, Cosmological models and science and religion: Lanczos potential theory The Weyl tensor can be generated differentially by a three index tensor: the Lanczos tensor, which was derived from a Lagrangian that was initially constructed to analyse the self-dual part of the Riemann tensor. An ongoing study is being carried out to investigate the mathematical and physical properties of the Lanczos tensor. In generating the Weyl tensor the Lanczos tensor acts as a potential - analogous to the electric tensor in electromagnetic theory. Non-linear partial differential equations applied to mathematical physics The Einstein field equations and the Weyl-Lanczos are highly non-linear and exact solutions are difficult to obtain. Current research is orientated in devising new techniques to establish solutions analytically. Twistor theory applied to Lanczos potential theory The purpose of this research is to utilise the techniques of twistor theory in order to carry out a qualitative and quantitative analysis of the Lanczos potential, which appears to have some connection with local twistor transport. Cosmological models The Ekpyrotic theory of the universe is being utilised in an attempt to discover how the cosmological constant might be affected following brane-world collisions. The cyclic affect of big bang to big crunch is expected to yield a finite cosmological constant at infinite future and past times. Science and Religion The concept of infinity is very well known in the field of science. However, exactly how this concept is manifest in the arts and religion remains a matter of great speculation. The purpose of this research is to identify the mechanism by which the concept of infinity can be reasonably understood and interpreted. |
