RESEARCH
My primary research interests lie in dynamical systems and algebraic
topology.
I am especially interested in the use of topological methods to study
qualitative
features of dynamics problems.
Dynamical Systems
Most of my recent work in dynamics has been in celestial
mechanics.
I have been working with Ken Meyer on understanding the topology of the
integral manifolds of the N-body problem, and learning how that
topology
influences the dynamics of the problem.
I am currently working with Christopher Pawlowski in the Sustainable
Environments Branch of the National Risk Management Research
Laboratory, United States Environmental Protection Agency. We are
exploring ways to mathematically define and compute ecological concepts
such as resilience, permanance and sustainability.
I have also worked with the Conley index. The index is a
generalization
of Morse theory, that allows topological methods to be used on dynamics
problems. I'm particularly interested in using the Conley index
information
to partially reconstruct the topology and dynamics of attractors.
For more on the Conley index, especially its use in deriving rigorous
dynamical
information from numerical explorations, visit the website of Konstantin
Mischaikow at Georgia Tech.
Mathematics and Manufacturing
I have worked with Sam Anand and the Computer Aided
Manufacturing Lab in the Department of Mechanical, Industrial
and Nuclear Engineering at the University of Cincinnati. Our work
together has focused on geometric modelling and optimization of
problems in manufacturing, including tolerancing, metrology, scheduling
Topology
My interests in algebraic topology are in fixed point theory (Nielsen
theory)
and critical point theory (Ljusternik-Schnirelmann category). Most of
my
work in Nielsen theory has dealt with computability issues.
For a full list of publications, including LaTeX and Postscript
files,
see my
publications list.
TEACHING
For the Autumn Quarter of 2006-07, I am teaching General Topology at
11:00 MWF in 807 Old Chemistry. Please see the blackboard site for more
information.
ADMINISTATION
I am currently serving as Associate Dean for Graduate Affairs in the McMicken
College of Arts and Sciences. I can be located in the college office
in 140 McMicken Hall, or at (513) 556-5895.
OTHER INTERESTS
My other professional interests are:
-
History of mathematics
-
Operations research and computational geometry
Some of my personal interests are:
-
History, especially American colonial history
-
Archaeology
-
Collecting antique maps. For a great source of antique maps, visit the
Heritage
Map Museum.
Americae from the 1607 Mercator/Hondius Minor Atlas
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