Mathematics Symposium: "Mathematics Awareness Month at UNO"
Mark J. Ablowitz,
"Waves, Waves, Waves, ... Waves Everywhere!"
Waves are common. Water waves, ocean waves, light waves, so typical
but yet so complex. Waves and their dynamics are widely studied by
scientists. In fact, mathematicians are in an advantageous
position. Even though the underlying physical descriptions may be
different, in many cases the dynamics satisfy the same or very similar
equations! In this lecture we will take a tour of some wave
phenomena. This will include: water waves in channels, tsunamis, great
undersea waves, waves in fiber optics, and waves constructed with
only 0's and 1's (the "game of life"). Although these systems may seem
very different, we will expose their important common elements. The
lecture will be general in nature, without any advanced mathematics
required. At times some equations will be presented as a vehicle to
explain and illustrate the fundamental similarities between the
systems.
Michael Bishop,
"Geographic Information Science for Studying Oceans and Complex System Dynamics
"
Our scientific understanding of oceanic, climate, and lithospheric
processes is depended upon mathematics, spatial modeling, and enabling
technologies of remote sensing, geographic information system
technology, and scientific visualization. Geographic information
science represents the integration of developments in these and other
disciplines, such that scientists are able to study the
spatio-temporal scale dependencies of processes and complex feedback
mechanisms. This talk will introduce important concepts of
geographic information science and provide example of how mathematics
and technology is used to collect data , extract environmental
information, and model complex dynamic systems. Some examples
include assessment of oceans and climate, thematic mapping, and
topographic evolution.
Lisa Boucher,
"Modeling Fossil Plant Form and Function"
Biologists and mathematicians have been attracted to the geometric
features and repeating patterns of plants and algae for
centuries. These features are linked to the developmental processes of
plants, which are controlled by genetics and the surrounding physical
world. Mathematical principles can be used to model and quantify
plant form, which can be especially useful when studying ancient
plants with no modern representatives. This presentation will explore
three examples from the field of paleobotany; studying the
biomechanics of fossil leaves using finite element analysis, using
elliptic Fourier analysis to quantify leaf shape for identification,
and the use of fractals in characterizing plant architecture.
Chris Farrow,
"The Logarithmic Spiral and the Golden Mean"
The oceanic chambered snail Nautilus has the shape of a logarithmic
spiral with golden mean proportions. First, the meaning of these
terms is explained. Then the mathematics of this relationship are
discussed in a simple geometric manner.
Jack Heidel,
"Solitary Waves in Shallow Water - A Nonlinear Phenomenon"
When John Russell observed a mass of water rolling along in the Union
Canal near Edinburgh, Scotland in 1838, the nonlinear science of
solitons was born. I will talk about the Korteweg-de Vries equation
which encodes such a wave and the unusual behavior of the solitary
wave solutions it possesses. The mathematics will be mostly informal
with lots of pictures.
Dora Matache,
"Creatures of the Ocean: Will They Become Extinct?"
In this talk we will show how a special type of stochastic processes,
called Branching Processes, can be used to model the perpetuation of
species. Extinction probabilities will be introduced and a formula for
their computation will be determined. We will illustrate by an example
how this formula can be used to model the chances of
extinction/survival.