Head of the Mathematical Analysis Group awarded Leverhulme Trust grant for multinational project

Professor Marco Marletta has been awarded the three-year grant for his project 'Maxwell and Drude-Lorentz, spectra and resonances: how hard can they be?'

The project is a multi-national collaboration between Professor Marletta and colleagues Professor Jonathan Ben-Artzi (Università degli Studi di Roma Tor Vergata), London Mathematical Society Whitehead Prize-winner Dr Sabine Bögli (Durham University), Dr Francesco Ferraresso (Università degli Studi di Verona), and the Director of the Mathematical Institute in Bern and Vice-President of the Swiss Mathematical Society, Professor Christiane Tretter.

Computational methods for approximately solving mathematical problems often rely upon the experience of their users to detect wrong answers, a famous example of which is the Moore-Penrose inverse of a matrix.

Many of these mathematical pathologies can be explained using Hansen Solvability Complexity Indices (SCI), and, within this framework, Professor Ben-Artzi and Professor Marletta have obtained major new results for classical problems in the last five years.

For example, can we reliably compute the sound of a Helmholtz resonator or recover the potential function in a Schrödinger equation by knowing the spectral data?

These problems remained open because standard theorems on numerical methods often concern 'towers of algorithms' (an infinite set of computations, each of which itself involves infinitely many computations) or a perfect knowledge of the data specifying the problem - neither of these scenarios is usually truly achieved.

The SCI classification of a problem, if it can be found, gives a measure of how hard the problem really is. This new project will investigate questions of solvability arising in mathematical models of electromagnetic waves.

Professor Marletta said: "I moved to Cardiff 23 years ago as a Leverhulme Fellow on sabbatical in the School of Computer Science and Informatics and was subsequently appointed to a position in the School of Mathematics. It is always a huge honour to receive recognition from the Leverhulme Trust, particularly for blue-skies research like this."