Graduate Group in Applied Mathematics
APPLIED MATHEMATICS is a subject area of immense breadth. As any
scientific field develops, it becomes more quantitative and requires
ever more sophisticated mathematics to formulate and solve its
basic problems. Nowhere is this more apparent than in the physical
sciences. For example, modern statistical mechanics is full of
important mathematical problems related to phase transitions and
stochastic dynamical systems. Differential geometry has become
the language of modern elementary particle physics. Quantum field
theory in physics has led to open problems in knot theory and
the mathematical field of topology. Important problems in the
chemical and engineering sciences lead to difficult nonlinear
differential equations that cannot be solved analytically. Often
these equations model fluids. This leads to important mathematical
problems related to the structure of solutions, and to numerical
and theoretical issues related to the problem of computing solutions
of these equations. Headway can only be made when the powerful
methods of mathematical analysis are brought to bear, and numerical
methods and asymptotic approximations are important. All of these
mathematical issues are part of current research projects being
carried out in the GGAM.
In the biological sciences, members of the GGAM are working on
developing mathematical models for describing biological systems
at the suborganismic, organismic and population levels. Differential
equations, optimization techniques, the mathematical theory of
stochastic differential equations and the theory of chaos in dynamical
systems are playing fundamental roles in this area. Specific research
projects at the organismic and suborganismic level include the
dynamical modeling of periodic and chaotic behavior in cell biology,
the control and regulation of ionic channels in excitable cells,
and the modeling of intermediary metabolism in living cells. Applications
of hydrodynamic theories to problems such as flow of water through
fish mouths, the effect of osmotic flows on plant morphology,
and medical imaging through magnetic resonance are also active
areas of research. At the population level the fields of resource
management, genetics, and population ecology are all represented
in the GGAM. Questions here include determining the forces responsible
for maintaining variability in populations, studying the dynamics
of structured populations, managing renewable resources, and understanding
animal behavior.
The GGAM is designed to facilitate the study of mathematical problems
that are important to science. Indeed, mathematics and science
go hand in hand, and there are many ways by which the scientist
is led naturally to the door of the applied mathematician.
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