David has devoted research effort to the broad area of applied mathematics, and specifically to the theoretical understanding of wave processes, since graduating in 1982 with a PhD in theoretical acoustics from Imperial College London. He currently holds the Beyer Chair of Applied Mathematics at the University of Manchester, a position occupied from 1885-1923 by Sir Horace Lamb and then subsequently by Sydney Goldstein, Sir James Lighthill and Fritz Ursell amongst others. He has published extensively in the areas of acoustics, fluid/structural interactions, nondestructive evaluation, fracture mechanics, linear and nonlinear elasticity, composite materials modelling, electromagnetism, water waves, aero- and hydro-acoustics and seismology. In recent years his research has diversified somewhat to also cover areas away from waves. For example, he has worked on topics as diverse as mathematical finance, nonlinear viscoelasticity, melting of debris-covered glaciers, and entrapment of meteorites in Antarctic ice.
David has been particularly concerned over the years with the development of new, or extensions of existing, mathematical techniques and has had a number of successes in this direction, ranging from novel methods for solving matrix Wiener-Hopf systems to new homogenisation techniques for wave propagation through solid composites. He has become increasingly interested in the application of such methods to problems in physics and engineering, and now works actively with a range of industrial partners. At present these include Thales UK, Dyson and NNSP. In 2010 he co-founded the Waves in Complex Continua (WICC) Group at Manchester, with Will Parnell, in order to facilitate both the fundamental and applicable research work that is being undertaken. The WICC Group now consists of some 20 members.
David plays an active role within the international mathematics community, having served on over thirty national and international working parties, panels and committees over the last decade. In particular, he was President of the Institute of Mathematics and its Application in 2008-9, Member of sub-panel UoA23 (Applied Mathematics) for the 2008 Research Assessment Exercise and Deputy Chair for sub-panel B10 (Mathematics) in the 2014 Research Excellence Framework, and Chair of EPSRC’s Mathematical Sciences Strategic Advisory Team (2014-15). He currently holds a Royal Society Wolfson Research Merit Award (2013-18) and is an Honorary Professor at the University of Edinburgh.
Over the years David’s enthusiasm for public engagement activities has grown steadily. He regularly offers mathematics talks of interest to school students and the general public, and ran the annual ‘Meet the Mathematicians’ outreach events for sixth form students with Chris Howls (Southampton). With Chris Budd (Bath) he organised in 2010 a training conference on ‘How to Talk Maths in Public’, and in 2014 co-chaired the inaugural ‘Festival of Mathematics and its Applications’. The latter was part of the Institute of Mathematics and its Applications’ 50th anniversary programme, and was an adventurous two-day meeting bringing together academics, mathematicians from outside academe (school teachers, industrialists, mathematicians in the financial sector etc.) , and over 1100 school students.
In 2014 David took on the role of Scientific Director of the International Centre for Mathematical Sciences (ICMS) in Edinburgh. This is a complementary centre to the Isaac Newton Institute, which offers mathematicians an excellent environment, primarily via short workshops, for the prosecution of their research. Since joining ICMS, David has tried to enhance ways for early career researchers (ECRs) to engage in activities and to meet leaders in their field, and to expand the number and range of interdisciplinary and knowledge transfer activities.