Harmonic Analysis and Applications

Professor Alan McIntosh will be presenting a special lecture for MSI's Alumni, friends and colleagues. The presentation will be followed by drinks, hors-d'oeuvres and a chance to meet and chat with the speaker and other members of the MSI.

Attendance at these special lecturers is by invitation only, so if you would like to attend, please register as a friend of MSI to recieve your invitation. 


Over 200 years ago, Fourier solved the heat equation in solids by representing the solution as a sum of sine functions.  This led to representations of a signal as a sum of waves of fixed frequency, and more recently as a decomposition into other basic components such as wavelets.  The theory behind such decompositions is known as harmonic analysis, which forms a deep and beautiful part of mathematics with surprisingly powerful applications.  In applications to the heat equation or the wave equation associated with discontinuous physical media, the decomposition can be correspondingly adapted.  Underlying such second order equations, there are often first order systems, such as the Cauchy-Riemann equations of complex function theory, and Maxwell's equations of electromagnetism.  It can be edifying to apply the harmonic analysis directly to the first order systems, rather than via the second order equations, as I shall outline in my presentation.

About the speaker

Alan McIntosh has worked at the Australian National University since joining its faculty 1999.  He has actively collaborated with international experts, research fellows and students on research in operator theory, harmonic analysis and partial differential equations.  For five years he was Head of The Centre for Mathematics and its Applications.  He attended school and university in Armidale where his father taught Philosophy at the University of New England.  He subsequently obtained a PhD from the University of California Berkeley, and then joined Macquarie University during its first year of teaching.  Collaborative research in Paris in 1980 led to a mathematical breakthrough, which boosted his subsequent career.  In 2002 he was awarded the Moyal Medal for Contributions to Mathematics. In May 2015 he was the joint recipient of the 2015 Hannan Medal for Research in Pure Mathematics by the Australian Academy of Science.