Research in the
Mathematical Sciences Institute
Links to recent research advancements in the MSI
Michael Barnsley - Taming the chaotic
Murray Batchelor - Maths helps unlock the secrets of early life
Conrad Burden - Mathematician in the vanguard of genomics revolution
Alan Carey, Adam Rennie - Weird new maths does not compute.
Lilia Ferrario - Illuminating the origin of neutron stars and black holes
Steve Roberts - Model to predict tsunami impact
Neil Trudinger, Xu-Jia Wang - Beautiful minds attract big awards
Other research highlights
Bioinformatics: Sue Wilson and her colleagues in the Centre for Bioinformation Science
(CBiS) investigated the reason that disease gene results are not
always replicable. Her important modelling result shows that the
cause may be due to researchers analysing each gene separately and
ignoring the complex interactions among the genes. ANU scientists now
are developing alternative genomic analyses of familial data.
The Monge mass transfer problem: The Monge problem of optimal mass
transfer has been one of the most famous problems in mathematics
during the last two centuries. Originally proposed by Monge in the
1780s in the prosaic form of finding the best way to move a pile of
soil with the least amount of work. A partial solution by Kantorovic
in the early 20th century led to the development of linear
programming. In 2001, Neil Trudinger and Xu-Jia Wang (Applied and Nonlinear Analysis) found a
simple approach to the problem and published the first correct proof.
Banach spaces: Very few Banach spaces
are known
for which the lattice of closed ideals in the Banach
algebra of all (bounded, linear) operators on the space is
fully understood. Indeed, since the late 60's the only such spaces were,
up to isomorphism, Hilbert spaces, and the classical sequence spaces.
The latter all have three element lattices. With colleagues in
Denmark and England, Rick Loy (Analysis
and Geometry) has added a new
member to this family, giving a space, built up from
finite-dimensional Hilbert spaces, whose lattice is a four element
chain.
Category theory: Amnon
Neeman (Algebra and Topology)
published a 449-page research monograph in the prestigious Annals of Mathematics Studies
series. The book proves many new theorems about triangulated
categories. Neeman also found a counterexample to a 40-year-old
result, which had been extensively applied in the literature.
Kato square-root problem: Alan McIntosh (Analysis and Geometry) was
recognised widely in the national press and international
arena for his part in the solution of a 40-year-old maths problem -
the Kato square root problem. This was achieved in collaboration with
mathematicians from France and the USA.
