MATHEMATICS COLLOQUIUM
Speaker: Michael Mascagni
Title: Quasi-Monte Carlo Methods: Where Randomness and
Determinism Collide.
Affiliation: Florida State University.
Date: Friday, November 3.
Place and Time: Room 101 - Love Building, 3:35-4:35 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract.
We will give a brief overview of Monte Carlo methods, methods for
solving problems that involve the use of random numbers.
Pseudorandom numbers are used in these simulations because they
mimic the behavior of "real" random numbers. However, there are
many Monte Carlo applications that do not really require randomness,
but instead need numbers that uniformly cover the sample space.
To meet these different requirements, quasirandom numbers have been
developed. These are numbers that are very evenly distributed, but
do not behave like truly random numbers. In fact, for certain
problems one obtains deterministic, not probabilistic, bounds for
Quasi-Monte Carlo methods. We present some of the fundamental
results about this deterministic method to solve random number
driven problems. We also describe some simple methods for
quasirandom number generation and discuss open problems in the
field.
This talk is more of a subject overview than a research
presentation. Dr. Mascagni will be in need of a large number of
graduate students for two projects that are about to start. These
project offer substantial opportunities to USM Scientific Computing
graduate students to find funded research opportunities working in
a state-of-the-art computational environment that includes access
to the latest high-performance computing hardware and software.
The research topics that make up these projects include Monte Carlo
methods, Quasi-Monte Carlo methods, pseudorandom number generation,
quasirandom number generation, high-performance computing, parallel
and distributed computing, interactive web design, web-enhanced
collaboration, descriptive statistics, and tests of randomness.
These projects will involve considerable collaborations with
colleagues at Sandia, Lawrence Livermore, and Los Alamos National
Laboratories as well as foreign colleagues in Salzburg, Austria and
Sofia, Bulgaria. Graduate students will be encouraged to form their
own collaborations with these groups and will be likewise encouraged
to visit them to further these collaborations.
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