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\mytitle{Lifting the Curse of Dimensionality \\ by Quasi-Monte Carlo Methods}

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\author{
\begin{tabular}{c}
	Frances Y. Kuo \\ %
    School of Mathematics and Statistics, University of New South Wales, Sydney, Australia \\
    \url{f.kuo@unsw.edu.au}
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High dimensional problems -- meaning problems with hundred or thousands or
even infinitely many continuous variables -- are now arising in many real
world applications. They present major challenges to computational
resources, and require serious mathematical efforts in devising new and
effective methods. This talk will begin with a contemporary review of
Quasi-Monte Carlo (QMC) methods, which offer tailored point constructions
for solving high dimensional integration and approximation problems by
sampling. By exploiting the smoothness properties of the underlying
mathematical functions, QMC methods can achieve higher order convergence
rates than standard Monte Carlo sampling, and moreover, QMC error bounds
can be independent of the dimension under appropriate theoretical
settings.

In recent years the modern QMC theory has been successfully applied to a
number of application areas including option pricing in financial
mathematics, maximum likelihood estimation in statistics, and PDEs with
random coefficients in computational physics and uncertainty
quantification. Rather than talking about these well-known popular
problems, this talk will present some ongoing works where we take QMC
methods to new territories such as quantum field problems in high energy
physics, neutron transport as a high dimensional PDE eigenvalue problem,
high frequency wave scattering in random media, and spatiotemporal
estimation in air pollution modelling.

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%This is a sample abstract for submitting a proposal for a talk or a poster presentation at CS2018. You should only submit the compiled PDF on the CS2018 web site \url{https://cs2018.sciencesconf.org/}.
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%\bibitem{Kantorovich42}
%L.~Kantorovich.
%\newblock On the transfer of masses (in russian).
%\newblock {\em Doklady Akademii Nauk}, 37(2):227--229, 1942.

%\bibitem{Monge1781}
%G.~Monge.
%\newblock M{\'e}moire sur la th{\'e}orie des d{\'e}blais et des remblais.
%\newblock {\em Histoire de l'Acad{\'e}mie Royale des Sciences}, pages 666--704,
%  1781.

%\end{thebibliography}





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