Research
The following are writeups of some research I've done,
in various states of completion and comprehensibility.
Unless otherwise specified, none of these papers have
been formally published (they would perhaps more properly
be called manuscripts). All files are in pdf format.
-
Environmental Evolutionary
Graph Theory
- Abstract.
We consider a simple stochastic spatial model of competition between two species.
The environment is represented by a graph with red and blue vertices,
which offer different levels of reproductive fitness to the two
species. We derive a simple closed-form solution for the fixation
probabilities in the special case where the graph is properly
two-colored.
- Remarks.
Most of this work was done during the
2007 REU
program at the
University of Illinois at
Urbana-Champaign, under the mentorship of
Robert Muncaster.
- Reconfigurable Systems and
Intractability
- Abstract.
Ghrist
and Peterson have investigated the properties
of a certain general class of reconfigurable systems, with an eye
to practical application. We show that in the general case,
these reconfigurable systems are powerful enough to represent
the rewriting rules of finitely presented groups, and therefore
fall prey to the existence of finitely presented groups with
unsolvable word problem.
- Remarks.
This paper was written as part of the
2008 REU program at UIUC,
under the mentorship of Kim
Whittlesey.
