Describing work in collaboration with Louise Dolan, I will discuss the scattering equations, originally introduced in 1972 by Fairlie and Roberts searching for new dual models, rediscovered by Gross and Mende in 1988, discussing the high energy behaviour of string theory, and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing remarkable formulae for tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons). We reformulate the scattering equations for N particles as a system of N -3 homogeneous polynomial equations in N - 2 complex variables, which are linear in each variable separately. The linearity of the equations enables their explicit solution in terms of the roots of a single-variable polynomial of degree (N-3)!, which can itself be explicitly constructed in terms of the Mandelstam variables formed from the momenta. The possible extension to one loop and the special case of four-dimensional space-time will also be briefly discussed.

Annual General Meeting of the London Mathematical Society. See http://www.lms.ac.uk/meetings/AGM04.html for further details.