Western Carolina
University
Department of Mathematics and
Computer
Science
Colloquium Series, 2004-2005
September 15th: Joseph Klerlein,
Dept.
of Math and CS, WCU
"What if Pascal visited a race track and met with the Easter Bunny?"
4PM, room TBA
Abstract: We consider two
different
problems, one from a horse race track and one for the Easter Bunny.
Surprisingly
we can find a "Pascal triangle like" solution for both.
February:
14th: Jeffery Lawson, Dept. of Math, Trinity University
"Finding relative equilibria on the
rigid body: An application of geometric mechanics"
Abstract:
Saari's Conjecture states that an N-body system (N
massive point particles attracted to each other by Newtonian
gravity) has a
constant moment of inertia if and only if the system is in relative
equilibrium,
that is, if the only solutions of the differential equations are
uniform rotations of the entire system.
Marsden's Conjecture generalizes the statement of Saari's
Conjecture general dynamical systems with symmetry. In recent
literature there have appeared N-body arrangements with non-Newtonian
gravity
that contradict Marsden's Conjecture.
In
this talk I'll reveal a novel counterexample to
Marsden's Conjecture where the dynamical
system under consideration is nothing more than a free rigid body in
three
dimensions. (``Free'' means zero
potential
energy.)
Examining
this counterexample leads us to a unique
method of identifying relative equilibria in the case where the
dynamical
system is any free Lie group (the most natural generalization of a
rigid body)
and allows us to repair Marsden's Conjecture in this context. This
result
illustrates the utility of geometrical approaches to solve problems in
dynamical systems with symmetry.
April 13th Sarah J. Greenwald, Dept. of
Math, Appalachian State University
"Mathematical Morsels from The Simpsons
and Futurama"
Abstract: Did you know that The Simpsons
and Futurama contain hundreds of instances of mathematics ranging from
arithmetic and number theory to geometry and calculus? Join us as
we present some of our favorite mathematical moments and explore the
related mathematical content, accuracy, and pedagogical value along
with the mathematical backgrounds of the writers. Special
emphasis will be placed on references related to this years Mathematics
Awareness Month on the Mathematics of the Cosmos. For more information,
check out simpsonsmath.com
Return
to WCU Math and CS Homepage
Maintained by despeaux@wcu.edu
Last Modified: 1 March 2005