Educational Background
Ph.D. in Mathematics, the George Washington University, 1995.
Dissertation: Approaches to Matroid Reconstruction Problems.
B.A. in Psychology and Mathematics, Mansfield University of Pennsylvania, 1988.
Mathematical Interests
I am mainly interested in discrete and combinatorial mathematics. Discrete mathematics is the
mathematics of finite (or usually at worst, countable) sets. Combinatorial
math is concerned with arrangements, orders, and patterns in such sets.
Many people call combinatorics the mathematics of counting. Although counting techniques
constitute one branch of combinatorics, I consider these as tools (of which there are many)
with which to explore order,
structure, and patterns in finite objects. Combinatorics itself is a
rather large field including the subfields of graph theory, order
theory, lattice theory, partition theory, coding theory, matroid theory, and others.
My specialization within the field of combinatorics is in matroid
theory. Matroids can be thought of as finite arrangements of points in space,
and they generalize the notion of independence found in Linear Algebra.
I am always impressed with the theory of matroids because of the way the field
brings together notions from just about every part of combinatorics
(especially graphs, lattices, and linear codes), as well as from linear algebra
and geometry. For more details about my research in matroid theory, see my papers:
"A Geometric Analog for Vertex Switching," submitted in 2004 to Discrete Mathematics.
"Unique Representability and Matroid Reconstruction," Advances in Applied
Mathematics, 30 (2003), 591 - 606.
"Characterizing Combinatorial Geometries by Numerical Invariants," with Joseph E.
Bonin, European Journal of Combinatorics, 20 (1999), 713 - 724.
"Techniques in Matroid Reconstruction," Discrete Mathematics, 170 (1997),
173-183.
I have worked with student research partners in matroid theory, and have directed
student research colloquia in probabilistic battlespace modeling, graphs of semigroups, election theory, admissions and recruitment problems, biostatistics, statistical
modelling in the
insurance industry, and systems of distinct representatives.
Computer Interests
Given the discrete bent of my mathematical interests, it is not surprising that
I find lots of areas of computer science interesting as well. I am
beginning a research program in robotics,
artificial life, and artificial intelligence, and I am looking for connections between
computer imaging and some of the matroid research I have been doing.
I also enjoy recreational programming, mainly in C++.
I have worked with student research partners in robotics and artificial intelligence, and have directed CS-related student projects in the areas of software engineering, genetic algorithms, robotics, and intelligent agents. When I taught at
Rockhurst University, I supervised projects
in Robotics and created a course in Software Engineering that I have since brought to
Susquehanna University. The course includes a 2nd Semester practicum using
a mobile robot (which SU was kind enough to purchase for the department) and simulating
a real contracting experience in software engineering.
Personal Interests
My wife Kelly and I have two sons, Rowan and Seanan (pronounced "Shah'-nan").
It is perhaps in questionable taste to refer to them as an interest, but they
do keep us busy (they are 9 and 7 years old, respectively).
I enjoy cooking (and eating). I am into mainly ethnic foods -- I
cook what I can't get at restaurants now that I've moved to
Selinsgrove, and my favorites tend toward the spicy side: Thai,
Indian, Ethiopian, Mexican -- although I also dabble in lots of
Chinese, Italian and several Northern European dishes. When I can get
really fresh fish, which is rare, I make my own sushi.
I love stories and storytelling, and enjoy writing when I get a chance (especially folktales
and ghost stories from various cultural perspectives).
When I lived in Washington, DC, some friends and I organized an interactive
storytelling group that was quite fun -- I would like to start such a group
here when I can find enough time and interested people.
I play my tuba as often as I get a chance (which
is too rarely these days).
Kelly and I brew beer and/or mead occasionally, and patronize the Selin's Grove
Brew Pub as many
Fridays as we can arrange it, considering the kids.
Sport-wise, I play racquetball and footbag, and my wife and I try to take at least one short ski vacation each year. There is a great racquetball community here at SU,
so I've been able to play quite a bit since the new sports complex opened.
Some people call footbag "Hackeysack", but Hackeysack is just one brand of footbags --
one of the
poorer brands in my opinion. Calling footbag Hackeysack is like
calling every tissue a Kleenex. Many people aren't aware of the
viciously competative 2-player footbag game played over a net.
It's impressive to watch someone jump up and spike a footbag over a five foot high
net with their feet. I bike to work as often as possible, and occasionally I get a chance to take longer rides. My wife and I like to go backpacking when we get the chance. Other than this, my
interest in sports is limited to watching the Superbowl every year
(mostly because I enjoy the food and drink that go along with
Superbowl parties).