Colloquia Patavina: Lifting the curse of dimensionality: numerical integration in very high dimensions

Martedi' 27 Settembre 2011 - Ian Sloan


Martedi' 27 Settembre 2011 alle ore 16:00 in aula 1A150 della Torre Archimede il Professor Ian Sloan (University of New South Wales, Sydney, Australia) terra' una conferenza della serie Colloquia Patavina.

La Commissione Colloquia
P. Ciatti, M.A. Garuti, M. Pavon, F. Rossi

Lifting the curse of dimensionality: numerical integration in very high dimensions

Ian Sloan (University of New South Wales, Sydney, Australia)

Richard Bellman coined the phrase “the curse of dimensionality” to describe the extraordinarily rapid increase in the difficulty of most problems as the number of variables increases. A typical problem is numerical multiple integration, where the cost of any integration formula of product type obviously rises exponentially with the number of variables. Nevertheless, problems with hundreds or even thousands of variables do arise, and are now being tackled successfully. In this talk I will tell the story of recent developments, in which within a decade the focus turned from existence theorems to concrete constructions that achieve the theoretically predicted results even for integrals in thousands of dimensions with many thousands of points. Suitable integration rules of this kind are now being applied to applications from mathematical finance and other fields.

-Breve curriculum
After schooling in Ballarat in Victoria, Australia, Ian Sloan completed physics and mathematics degrees at Melbourne University, a Master's degree in mathematical physics at Adelaide, and a PhD in theoretical atomic physics (under the supervision of HSW Massey) at the University of London, finishing 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 computational mathematics . Since making that change he has published 200 papers on the numerical solution of integral equations, numerical integration and interpolation, boundary integral equations, approximation theory, 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. 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 completed a term as Chair of the Chemistry, Mathematics and Physics Panel of the Australian Research Council and member of the ARC's Research Grants Committee, and is a former President of the Australian Mathematical Society .
He was elected a Fellow of the Australian Academy of Science in 1993. In 1997 he was awarded the ANZIAM Medal by 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. In 2002 he was awarded the Szekeres Medal of the Australian Mathematical Society, and in 2005 was awarded the Information Based Complexity Prize. In 2008 he was appointed an Officer of the Order of Australia (AO).
He is a member of the editorial board of a number of international journals, including SIAM Journal of Numerical Analysis, Numerische Mathematik, Advances in Conmputational Mathematics, Journal of Integral equations and Applications and the new International Journal of Geomathematics, and is a Senior Editor of the Journal of Complexity.
From 2003 to 2007 he was President of the International Council for Industrial and Applied Mathematics, Before that he was the Chair of the International Program Committee for ICIAM 2003, the fifth International Congress on Industrial and Applied Mathematics, held in Sydney in 2003. He is currently Deputy Director of MASCOS, the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.

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