Abstract
The fourth dimension always fascinates: given that we live in a three-dimensional world, how can we imagine a fourth dimension? Many attempts to imagine a fourth dimension have been made in popular culture, not always successfully. Yet computational scientists nowadays routinely perform calculations not just in four dimensions, but even in hundreds or thousands of dimensions, thereby illustrating the power of mathematics to take us where imagination cannot go. When the dimensionality is large we meet a very real challenge, which Richard Bellman called the \curse of dimensionality". In this talk I will explain in non-technical terms the ideas that allow us, when the conditions are right, to transcend the curse of dimensionality, and so to calculate effectively and painlessly in very high dimensions.
About the Speaker
Professor Ian Sloan completed his PhD in theoretical atomic physics (under the supervision of HSW Massey) at the University of London in 1964. After a decade of research on few-body collision problems in nuclear physics, and publishing some 35 papers in the physics literature, his main research interests shifted to numerical analysis. Since making that change he has published some 200 papers on the numerical solution of integral equations, numerical integration and interpolation, boundary integral equations, multiple integration, continuous complexity theory and other parts of numerical analysis and approximation theory.
He was employed by Australia's CSR Company from 1961 to 1965, before joining the University of New South Wales as a Lecturer in 1965. After several promotions, he was appointed to a Personal Chair in Mathematics in 1983. He was Head of the School of Mathematics from 1986 to 1990 and from 1992 to 1993. He has completed a term as Chair of the Chemistry, Mathematics and Physics Panel of the Australian Research Council, and a member of the ARC's Research Grants Committee, and is a former President of the Australian Mathematical Society. From 2003 to 2007 he was the President of the International Council for Industrial and Applied Mathematics.
He was elected a Fellow of the Australian Academy of Science in 1993. In 1997 he was awarded the ANZIAM Medal by the antipodean equivalent of SIAM, known as Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), and in 2001 was awarded the Thomas Ranken Lyle Medal of the Australian Academy of Science. He is a member of the editorial board of a number of international journals. In 2008 he was appointed an Officer of the Order of Australia.
He is currently a Scientia Professor at the University of New South Wales, and a Chair Professor under the Distinguished Scholar Scheme at the Hong Kong Polytechnic University.
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