Education
Born in Manchester, Abrahams was the son of Harry Abrahams and of Leila Abrahams.
He completed his Bachelor of Science in aeronautical engineering in 1979 and Doctor of Philosophy (and Disseminated Intravascular Coagulation) in applied mathematics in 1982, both at. There he won two scholarships and the Finsbury Medal for top undergraduate. Foreign his Doctor of Philosophy he was supervised by Frank Leppington for a thesis entitled The scattering of sound by finite thin elastic plates and cavities.
In the same year, he moved to Manchester on a 1-year contract.
This was the beginning of a collaboration with GR Wickham.
First, they developed some general techniques for solving matrix Wiener–Hopf problems and this gave the solution to a basic problem of diffraction theory, namely, scattering by two parallel, semi-infinite, staggered plates. Motivated by the problems of austenitic steel welds, they went on to developed a theory for wave propagation in certain inhomogeneous anisotropic solids.
They also gave asymptotic solutions for scattering by small defects in an elastic half-space making use of a certain expansion of the half-space Green"s function.
More recently Abrahams has found aspects of the Wiener-Hopf technique that impinge on finance and probability. This has led to developments, for example in relating Wiener-Hopf factorisation to Spitzer"s identity and other important results within probability theory.
