Conference in honour of
Ian Sloan on the occasion of his 80th birthday,

17-19 June 2018, UNSW, Sydney, Australia.

Sunday 17 June | Monday 18 June | Tuesday 19 June | |

8:30 - 9:00 | (* by invitation only) | Breakfast | |

9:00 - 9:30 | Tony Guttmann | ||

9:30 - 10:00 | James Sethian | ||

10:00 - 10:30 | Honorary degree conferral* | Nalini Joshi | |

10:30 - 11:00 | Honorary degree conferral* | Coffee | |

11:00 - 11:30 | Honorary degree conferral* | Ronald Cools | |

11:30 - 12:00 | Morning tea* | Douglas Arnold | |

12:00 - 12:30 | Morning tea* | Mark Ainsworth | |

1:00 - 2:00 | Registration and lunch | Lunch | |

2:00 - 2:30 | Opening - Emma Johnston Welcome - Bruce Henry |
Fred Hickernell | |

2:30 - 3:00 | Edward Redish | Markus Hegland | |

3:00 - 3:30 | Wolfgang Wendland | Henryk Wozniakowski | |

3:30 - 4:00 | Coffee | Coffee and farewell | |

4:00 - 4:30 | Mile Giles | ||

4:30 - 5:00 | Linda Petzold | ||

5:00 - 5:30 | Dinner | Ivan Graham | |

5:30 - 9:00 | Dinner |

Edward Redish
University of Maryland, USA

In 1971, I was a recently minted mathematical physicist hunting for a future.
Along came a visitor from the other side of the world bearing a set of new tools and new ways
of mathematical thinking that changed how I thought about complex nuclear reactions.
Twenty years later, I transitioned to a new career in which I think about the role math plays
in scientific thinking and how “mathematicians and physicists are two disciplines separated
by a common language.” I’ll provide reminiscences and examples of what I’ve learned as a
mathematical physicist and as a cognitive education researcher.

Wolfgang Wendland University of Stuttgart, Germany

The minimal energy problem for nonnegative charges on a closed surface $\Gamma$ in $\mathbb{R}^3$ goes back to C.F.~Gauss in 1839.
The corresponding Riesz kernel is then on $\Gamma$ weakly singular. More general, in $\mathbb{R}^n, n\geq 2$, the constructive and
numerical solution of minimizing the energy relative to the Riesz kernel then defines on $\Gamma$ a weakly singular single layer
boundary integral operator. The construction and numerical solution of minimizing the corresponding energy then provides the
distribution of charges on $\Gamma$ whose single layer potential is the solution of the Dirichlet problem inside $\Gamma$.
For more general Riesz kernels the corresponding minimizing problem leads to a charge distribution which provides the density
of Sloan’s integration points on $\Gamma$. If the surface consists of two separate parts $\Gamma_1$ and $\Gamma_2$ with
positive charges on $\Gamma_1$ and negative charges on $\Gamma_2$ then the minimizing charge distribution can be approximated
by piecewise constant charges via a Galerkin-Bubnov method. Wavelet matrix compression is applied for solving the discrete system.
This is joint work with Helmut Harbrecht (Basel), Günther Of (Graz) and Natalia Zorii (Kiev).

Mike Giles ,
University of Oxford, UK

One noteworthy aspect of Ian Sloan's career is his switch from theoretical physics to computational mathematics. In this talk I will discuss my own mid-career switch from CFD (computational fluid dynamics) to mathematical finance and Monte Carlo methods, with a visit to Ian in UNSW in early 2007 being a key part of my switch.

Linda Petzold, UCSB, USA

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within
a neuronal network to generate precise system-wide circadian rhythms. In past work we have
inferred the functional network for synchronization of the SCN. In recent work we have inferred
the directionality of the network connections. We discuss the network structure and its
advantages for function.

Ivan Graham University of Bath, UK

In late 1975 I received a very enthusiastic aerogramme from Ian Sloan telling me that
"he and his collaborators had just discovered some exciting new numerical
methods for solving integral equations", and offering me a PhD scholarship to work with
him on this at UNSW. Going to Sydney in 1976 to work with Ian was probably the most important
decision of my career and I'm pleased to say that we have kept in close touch and have continued
to work together down the years. In fact recently some of the things we were working on in 1976
became useful again in the analysis of uncertainty propagation in reactor modelling, an
industrial project I've been doing with Wood plc in the UK. I'll talk about this and, more
generally, I'll talk about uncertainty quantification for various PDE models and how recent work by
Ian and a number of other collaborators on high dimensional integration has allowed us to make
substantial progress in this area.

Tony Guttmann
Melbourne, Australia

There are n! permutations of the integers 1,2,...,n. We say that a permutation *avoids* a given
sub-permutation (called a *pattern*) if there is no sub-sequence of the permutation with digits
in the same relative order as the digits in the pattern. Thus 1,2,3,4,5 avoids the pattern 2,1
as there are no two integers in decreasing order in the permutation. However 1,3,4,2,5 does
not avoid the pattern, as the pairs 3,2, and 4,2 are both in decreasing order. We will
describe some open questions, and discuss some numerical methods for exploring them.

James Sethian
University of Berkeley, USA

Moving interfaces appear in a large variety of physical phenomena, including mixing fluids,
industrial printers, medical images, and foamy fluids. One way to frame moving interfaces is
to recast them as solutions to fixed domain Eulerian partial
differential equations, and this has led to a collection of PDE-based techniques, including
level set
methods, fast marching methods, and ordered upwind methods. These techniques easily accommodate
merging
boundaries and the delicate 3D physics of interface motion. We will give a brief overview
of these methods, and then talk about a few selected new applications from fluids, materials science,
and image analysis.

Nalini Joshi
University of Sydney, Australia

Symmetry is an essential part of our description of the world. The quality of being made up of exactly similar parts facing each other is all around us: one day reflects another and the days fill out the year in the same way that similar hexagonal compartments fill out a honeycomb. The mathematical description of symmetries is built from only two operations: reflections and translations. In two dimensions, these give rise to triangular, hexagonal and square tilings of the plane. But in higher dimensions, many more tiling patterns are available. One of the many questions that arise is how to go from higher dimensional tilings to two dimensional ones. I will show how to use these ideas to link two major theories that arise in mathematical physics.

Ronald Cools KU Leuven, Belgium

In 1991 Ian invited me to Sydney to join forces, and in 1992 I went.
At that time one of his research passions were lattice rules for periodic
functions. Mine was cubature formulas that are exact for trigonometric
functions. Together we investigated minimal cubature formulas, and we
obtained rules for arbitrary polynomial degrees of precision with free
parameters. These are all equal weight rules with points shifted in a
particular way. Within this continuum there are lattice rules. So we
were both happy with the result. Why it took 4 more years before the
paper appeared in print is another story.
In a series of papers that started at an Oberwolfach meeting in 1992,
Ian and Harald Niederreiter modified lattice rules for non-periodic
function. They modified the weights and kept the points. Dirk Nuyens
and I picked up this thread for the occasion of Ian's 80th birthday.

Douglas Arnold,
University of Minnesota, USA

From our first encounters with partial differential equations and
Fourier analysis, we encounter eigenfunctions of elliptic operators
which are oscillatory and global: sines, cosines, Bessel functions,
and so forth. But when the coefficients of the PDE are not smooth
but disordered, an entirely different sort of eigenfunction appears:
spiky and highly localized. Such localization is highly relevant in
physical applications, especially in quantum mechanics. A large body
of mathematics has been developed to explain it, but many aspects of
localization remain mysterious. In particular, most known results
are probabilistic, providing statistical information for a class or
operators with random coefficients, but not information specific to
a particular realization of such an operator. We will describe a new
and very different perspective on localization. The new viewpoint is
deterministic, enabling us, for the first time, to deduce the localized
spectrum of a disordered operator without actually calculating its
eigenfunctions and eigenvalues. This approach holds out the promise
of harnessing disorder to create devices and materials with new and
desired properties.

Mark Ainsworth,
Brown University, USA

Recent years have seen a surge of interest in fractional partial differential equations driven, in part, by the
desire to develop models that are able to more accurately model systems which exhibit behaviour including
sub-and super-diffusion. In the current work, we shall discuss a fractional version of the Swift-Hohenberg
equation. The Swift-Hohenberg equation is a non-linear parabolic PDE which is known to have solutions
display pattern formation, and which has been used in the physics literature to develop macroscopic models
for crystals known as "phase field crystals." We consider a fractional version of the Swift-Hohenberg
equation (FSHE) which gives a non-linear fractional parabolic problem. In particular, we show that FSHE
is well-posed and admits a unique solution; develop a Fourier-Galerkin scheme and obtain error estimates;
analyse pattern formation properties and discuss the use of FSHE to develop fractional phase
field crystal models. This is joint work with Zhiping Mao (Brown University).

Fred Hickernell IIT Chicago, USA

Ian Sloan has been a key developer and proponent of integration lattices for numerical
computation. His 1994 monograph has over 700 citations, and his more recent 2013 Acta Numerica
article has over 200 citations. This talk highlights how well-chosen integration lattices can speed
up numerical multidimensional integration in contrast to tensor product rules and simple Monte
Carlo. It also describes recent work sampling with integration lattices when performing Bayesian
cubature, where the integrand is assumed to be an instance of a Gaussian random process.

Markus Hegland ANU, Australia

Ian Sloan has made substantial contributions to high dimensional quadrature
and approximation which include the establishment of quasi Monte Carlo Methods,
and results about the ANOVA decomposition of functions. Combining ideas from
algebra and analysis he and his collaborators have been able to control the
curse of dimensionality to a large extent. He has actively nurtured Australian
research in high-dimensional computing, and the development of
sparse grid approximation. Sparse grids have been used for the solution
of differential equations and recently in uncertainty quantification and
fault-tolerant algorithms. In my presentation I will review some of the
development of the sparse grid combination technique and its foundations in
algebra, extrapolation and ANOVA decompositions.

Henryk Wozniakowski
Columbia University, USA and
University of Warsaw, Poland

I will try to summarize over 25 years of our collaboration and friendship with Ian Sloan. Most of our papers deal with tractability of multivariate
problems such as multivariate integration and approximation. I will cite
the results of our first and last paper.