David Abrahams (mathematician)
Encyclopedia
Ian David Abrahams is an English Mathematician, currently Beyer Professor of Applied Mathematics
at the University of Manchester
. He has acted as vice president, and as of January 2008 is president, of the Institute of Mathematics and its Applications
.
, Abrahams was the son of Harry Abrahams and of Leila Abrahams.
He completed his BSc
in aeronautical engineering in 1979 and PhD
(and DIC
) in applied mathematics
in 1982, both at Imperial College London
. There he won two scholarships and the Finsbury Medal for top undergraduate. For his PhD 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.
Abrahams's leisure interests include motorcycling and he owns a 1977 Triumph Bonneville
T140V, as well as a 1000cc Moto Guzzi
.
Beyer Chair of Applied Mathematics
The Beyer Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The endowment came from the engineer Charles Frederick Beyer, a generous supporter of the University....
at the University of Manchester
School of Mathematics, University of Manchester
The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an undergraduate intake of roughly 400 a year and another 200 postgraduate students...
. He has acted as vice president, and as of January 2008 is president, of the Institute of Mathematics and its Applications
Institute of Mathematics and its Applications
The Institute of Mathematics and its Applications is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics ....
.
Education
Born in ManchesterManchester
Manchester is a city and metropolitan borough in Greater Manchester, England. According to the Office for National Statistics, the 2010 mid-year population estimate for Manchester was 498,800. Manchester lies within one of the UK's largest metropolitan areas, the metropolitan county of Greater...
, Abrahams was the son of Harry Abrahams and of Leila Abrahams.
He completed his BSc
Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
in aeronautical engineering in 1979 and PhD
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
(and DIC
Diploma of Imperial College
The Diploma of the Imperial College is an academic certificate awarded by Imperial College London to its postgraduate students upon graduation. Until recently, Imperial was part of the University of London and Imperial College bestowed the University of London's degrees as well as its own...
) in applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
in 1982, both at Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
. There he won two scholarships and the Finsbury Medal for top undergraduate. For his PhD 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
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
theory, namely, scattering by two parallel, semi-infinite, staggered plates. Motivated by the problems of austenitic steel
Austenite
Austenite, also known as gamma phase iron, is a metallic non-magnetic allotrope of iron or a solid solution of iron, with an alloying element. In plain-carbon steel, austenite exists above the critical eutectoid temperature of ; other alloys of steel have different eutectoid temperatures...
welds
Welding
Welding is a fabrication or sculptural process that joins materials, usually metals or thermoplastics, by causing coalescence. This is often done by melting the workpieces and adding a filler material to form a pool of molten material that cools to become a strong joint, with pressure sometimes...
, 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
Green's function
In mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions...
.
More recently Abrahams has found aspects of the Wiener-Hopf
Wiener-Hopf
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed...
technique that impinge on finance and probability
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. This has led to developments, for example in relating Wiener-Hopf factorisation to Spitzer’s identity and other important results within probability theory.
Personal life
In 2004, Abrahams married Penelope Lawrence Warwick with whom he has one daughter and two step sons.Abrahams's leisure interests include motorcycling and he owns a 1977 Triumph Bonneville
Triumph Bonneville
The Bonneville is a range of British motorcycles, made in three different production runs from 1959 to 1983, and 1985 to 1988, by the now-defunct Triumph Engineering in Meriden; and since 2001, by Triumph Motorcycles in Hinckley. It is named after the Bonneville Salt Flats, Utah, where Triumph and...
T140V, as well as a 1000cc Moto Guzzi
Moto Guzzi
Moto Guzzi is an Italian motorcycle manufacturer. It is one of seven brands owned by Piaggio.Established in 1921 in Mandello del Lario, Italy, the company is noted for its central historic role in Italy's motorcycling manufacture, its prominence worldwide in motorcycle racing, and a series of...
.