Tutorial Fellow in Mathematics, Wadham College

My main work is in the mathematics of fundamental physics.  Since the 1970s I have contributed to the twistor programme for physics initiated by Roger Penrose (who is an Emeritus Fellow of Wadham College). Twistor geometry involves a radical new description of space and time, and has the potential to transform our understanding of the universe as radically as Einstein did a century ago. My own contribution involves studying certain large-dimensional complex contour integrals, called twistor diagrams, which give a completely new description of how elementary particles interact.

Twistor theory gained new impetus in 2003, when the leading mathematical physicist Edward Witten made new connections between twistor geometry and other current developments in physics. Since 2005 I have built on these connections to show the value of  twistor methods for understanding the very complicated structures involved in particle interaction. Since 2008 my ideas have been taken further by the leading physicist Nima Arkani-Hamed. Thanks to his and other generous invitations I have made extended visits to the Institute for Advanced Study at Princeton, and other research centres. It has been particularly rewarding to see twistor-based ideas taken up by a new generation of graduate students and post-doctoral researchers.

A second body of work springs from my interest in the British mathematician Alan Turing (1912-1954), who was the founder of modern computer science, and the chief scientific figure in Second World War code-breaking. My biography Alan Turing: the enigma (1983) has been translated into several languages (winning an Italian literary prize), and a Chinese edition is imminent. It has also been dramatised (as Breaking the Code) for stage and television. My work shows how the historical roots of modern technology lie in mathematical discovery. But my narrative weaves this together with Alan Turing's life and consciousness as a gay man, and indeed much else. Since 1995 I have maintained an extensive Turing website to complement the book and reach a global public. It is gratifying that (partly thanks to the Web) the unusual standpoint I adopted in 1983 has become more widely acceptable and that the book has inspired other writers and creative endeavours around the world.

Starting with a short book in a series on The Great Philosophers (1997), I have also written further papers on the history and philosophy of computation. The year 2012 marks the centenary of Alan Turing's birth, and I am participating in a number of celebratory events, including a special meeting of the American Mathematical Society, and of Computability in Europe.

I have taught mathematics at Wadham College since 1986, and was elected a Fellow in 2007. I was appointed Dean in 2011.

Research group
Mathematical Physics group

Courses Taught
I am tutor for a wide range of courses in pure and applied mathematics, both in the College and for inter-collegiate classes. I have also several times given the University lectures in General Relativity.

Some recent publications
Twistor diagram recursion for all gauge-theoretic tree amplitudes (2005)

Twistor diagrams for all tree amplitudes in gauge theory: a helicity-independent formalism (2006)

Scattering amplitudes for eight gauge fields (2006)

Eliminating spurious poles from gauge theoretic amplitudes (2009)

The box integrals in momentum-twistor geometry (2010)

(With N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka) A note on polytopes for scattering amplitudes (2010)

New expressions for gravitational scattering amplitudes (2011)

The Essential Turing, Notices of the American Mathematical Society, 53, 1190 (2006), also in Chinese: Mathematical Advances in Translation, 27 (2008).

Alan Turing: the logical and physical basis of computing, for British Computer Society symposium (2008)

Alan Turing, Logical and Physical, opening essay in New Computational Paradigms, eds. S. B. Cooper, B. Löwe, A. Sorbi (Springer, 2008)

What did Alan Turing mean by 'machine', in The Mechanical Mind in History, eds. P. Husbands, O. Holland and M. Wheeler (MIT Press, 2008)

In retrospect: Gödel's Proof, Nature 454, 829 (2008)

Alan Turing: entry in the Princeton Companion to Mathematics (2008)

Fair play for machines, Kybernetes 39, 441 (2010)

(With C. V. Sukumar) Bernoulli, Euler, permutations and quantum algebras, Proc. Roy. Soc. 463, 2401-2414 (2007).  See my on-line introduction.

(With C. V. Sukumar) Quantum algebras and parity-dependent spectra, Proc. Roy. Soc. 463, 2415-2427 (2007)

One to Nine, Short Books (2007)

Links

Twistor diagrams

Alan Turing

Personal home page

Wikipedia