Abstract

The first industrial revolution was about harnessing physics, the second industrial revolution, unfolding in front of our eyes, is about information: its collection, transmission, compression, coding, encryption and decryption and, in particular, its understanding. This has profound implications for tomorrow’s mathematics, which are already felt today. This talk will examine emerging themes in mathematical sciences which address the challenge of information, in particular mathematical image processing (how to use differential equations and variational problems to analyse, interpret, manipulate and enhance digital images) and compressed sensing (how to be smart by collecting less data yet analysing them better, taking advantage of their innate sparsity).

Dr Hansen, recently appointed a University Lectureship in the Mathematics of Information. works in the area of computational harmonic analysis with emphasis on sampling theory and compressed sensing. He is a Royal Society University Research Fellow and previously held a von Karman Instructorship at Caltech and a Research Fellowship at Homerton. His non-mathematical collaborators include the University of Cambridge Magnetic Resonance Research Centre. Professor Iserles’ research interests include aspects of the numerical solution of differential equations and other areas of computational mathematics. He is co-Director of the Cambridge Centre for Analysis (a joint initiative of the two Cambridge Mathematics Departments) and was a winner of the 2012 David Crighton Medal awarded jointly by the London Mathematical Society and the Institute for Mathematics and its Applications.