My Expertise
Boundary integral equations, high dimensional integration and approximation, informationbased complexity, multivariate approximation theory, numerical analysis of integral and partial differential equations
Fields of Research (FoR)
Numerical Solution of Differential and Integral Equations, Numerical Analysis, Approximation Theory and Asymptotic Methods, Analysis of Algorithms and ComplexitySEO tags
Biography
ABOUT ME
After schooling in Ballarat in Victoria, Australia, I 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 fewbody collision problems in nuclear physics, and publishing some 35 papers in the physics literature,...view more
ABOUT ME
After schooling in Ballarat in Victoria, Australia, I 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 fewbody collision problems in nuclear physics, and publishing some 35 papers in the physics literature, my research interests shifted to computational mathematics . Since making that change I have published more than 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.
My first employment from 1961 to 1965 was by Australia's CSR Company (who sent me to London to do a PhD), before I joined the University of New South Wales as a Lecturer. Highlights of the early UNSW years involved in physics research were a threemonth visit to India on a Leverhume Fellowship and a yearlong sabbatical at the University of Maryland, College Park, supported by a Senior Fulbright Fellowship. After several promotions, I was appointed to a Personal Chair in Mathematics in 1983. I was Head of the School of Mathematics from 1986 to 1990 and then from 1992 to 1993. I am currently both Emeritus Professor and parttime Professor in the School of Mathematics and Statistics at UNSW.
I was for a period Chair of the Chemistry, Mathematics and Physics Panel of the Australian Research Council, and member of the ARC's Research Grants Committee. I have been President of the Australian Mathematical Society and also Chair of its Division of Applied Mathematics (now ANZIAM).
I was elected a Fellow of the Australian Academy of Science in 1993. and in 1997 he awarded the ANZIAM Medal by Australian and New Zealand Industrial and Applied Mathematics (ANZIAM). In 2001 I was awarded the Thomas Ranken Lyle Medal of the Australian Academy of Science, and in 2002 the Szekeres Medal of the Australian Mathematical Society. In 2005 I was awarded the Information Based Complexity Prize. In 2008 I was appointed an Officer of the Order of Australia (AO), and in 2018 was awarded an Honorary Doctorate of the University by the University of New South Wales.
I have been 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, the International Journal of Geomathematics, Foundations of Computational Mathematics and the Journal of Complexity.
From 2003 to 2007 I was President of the International Council for Industrial and Applied Mathematics, Before that I 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. I was a Chief Investigator and then Deputy Director of MASCOS, the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems. I am currently President of the Royal Society of NSW.
Education
 BSc in Physics (Melbourne 1958)
 BA (Hons) in Mathematics (Melbourne, 1960)
 MSc in Mathematical Physics (Adelaide, 1961)
 PhD in Theoretical Physics (London, 1964).
RESEARCH
Research Goals
 Excellence in computational mathematics at an international level
Research in Detail
After an early research career in theoretical physics, I turned to computational mathematics, which I think of as the rigorous application of mathematics to develop new and improved methods for the approximate solution of mathematically challenging problems in science, engineering, and other fields {mathematical finance being a key new area). I have worked with integral equations, partial differential equations, the complexity of continuous problems, numerical integration, and approximation and other areas. Of particular interest these days are problems involving a very large number of continuous variables (where we working to overcome the “curse of dimensionality), and problems of integration and approximation over spheres, often coming from geophysics. .
Research Grants

 ARC Discovery Grant 2011 – 2013 (jointly with Frances Kuo) Very High Dimensional Computation – the New Frontier in Numerical Analysis
 ARC Discovery Grant 2012 – 2014 (jointly with Josef Dick) Mathematics in the Round – the Challenge of Computational Analysis on Spheres
Current Student Projects (PhD and Honours)
Numerical analysis of high dimensional computation.
Approximation schemes on spheres
The effect of filtering on quality of approximation.
Supervision Opportunities/Areas
There are good opportunities for PhD supervision for students with a strong background in mathematics, especially analysis
Advice for prospective students
The Computational Mathematics Group at UNSW is a vibrant group, with excellent international connections. It is an attractive destination for enthusiastic students with strong mathematical talents.
TEACHING & OUTREACH
Professional affiliations and service positions
I was formerly President of the International Council for Industrial and Applied Mathematics
Elected Fellow of SIAM, 2009
Elected Fellow of the American Mathematical Society, 2012
AWARDS & ACHIEVEMENTS
Elected Fellow of the Australian Academy of Science, 1993
Scientia Professsor UNSW, 1999
Lyle Medal of the Australian Academy of Science 2001
Szekeres Medal of the Australian Mathematical Society 2002
Information Based Complexity Prize 2005
Appointed Officer of the Order of Australia, 2008
Elected Fellow of the Royal Society of new South Wales, 2014
My Grants
"Innovations in spherical approximation  construction analysis and applications. (I H Sloan, E. Saff (Vanderbilt) and H. Wendland (Oxford)).
"Very high dimensional computation  the new frontier in numerical analysis" (I H Sloan, F Y Kuo, M. Griebel (Bonn), and H. Wozniakowski (Warsaw and Columbia)).
2018  2020 :Uncertainty on spheres and shells: mathematics and methods for applications". (Q T Le Gia, I H Sloan and Brzezniak) DP180100506
2018  2020 "Towards a science of highdimensional computation" {F Y Kuo and I H Sloan) DP180101356
2021  2023 "High dimensional computation and uncertainty" (F Y Kuo and I H Sloan) DP210100831
Location
University of New South Wales
Sydney NSW 2052
The Red Centre
Room 2072