


I grew up in central Florida, the son of
citrus farmers. I went to college at the University
of North Carolina at Chapel Hill, where I
originally intended to become a medical doctor.
But I became fascinated with mathematics as a student
and changed career paths. I completed an
undergraduate senior thesis (studying among other things
the picture you see at left) under the direction of Jane
M. Hawkins and graduated with my bachelor's degree
in 2000.
I went on to earn a Ph.D. in mathematics from the University
of Maryland in May 2006, completing my thesis
under the direction of the late Daniel
J. Rudolph.
Since completing my education, I held postdoctoral
positions at Northwestern
University and Swarthmore
College before joining the Ferris State faculty in
2012.
Click here for
my curriculum vitae.


I
study ergodic theory. To get an idea of what this
is, consider the following example. Suppose you
were interested in determining the "average" temperature
of water in a lake. One thing you could do is put
a bunch of thermometers at various spots in the lake,
take readings from each of these thermometers (at the
same instant), and average these readings. Another
thing you could do is to take one thermometer, attach it
to a fish and take readings from this one thermometer
every minute, averaging the readings you get.
A key principle of ergodic theory is that these two
methods of averaging will coincide, so long as the
movement of the fish is reasonable (by "reasonable", I
mean that the fish should eventually swim in all parts
of the lake). Ergodic theory concerns itself
(among other things) with describing the "average"
behavior of systems that change over time by examining
probabilistic and statistical properties of dynamical
systems (a dynamical system is any mathematical model
for a quantity that changes as time passes; think of the
location of the fish as the dynamical system in the
above example). Historically speaking, the
motivating problems of ergodic theory come from physics,
but ideas in ergodic theory have been applied in other
areas of mathematics as well as in biology, chemistry,
economics, and other fields. For more on dynamical
systems and ergodic theory, click here
and here.
My past work includes:
 complex dynamics of quadratic
rational maps
 descriptive dynamics and ergodic
theory of continuous semigroup actions
 applications of ergodic theory to
number theory, particularly the complexity theory of
multiple ergodic averages
My current work explores the "speedup equivalence" of
actions of commuting transformations in both the
measurepreserving and topological categories.
Outside of ergodic theory, I am also interested in
connections between math and games, and in applications
of mathematics and statistics to sports analytics, and
have worked with students on projects in these areas in
the past.
Click here for my papers and
click here to see slides from
my talks.


I
am always interested in working with students in
independent study courses and on research
projects.
In the past I have directed independent studies in:
 dynamical systems and
chaos
 measure theory and
Lebesgue integration
 vector calculus and
differential geometry
 mathematical biology
 topology
Several of my students have presented posters at
local, regional and national events and three have
had papers published (see below).
If you are interested in an independent study or
undergraduate research project (I have lots of
ideas, and I am also willing to learn new math to
meet your interests), email
me or stop by my office.


Papers
by my undergraduate students

Jonathon
Wilson, "Entropy
of LEGO(R) jumper plates", to
appear in The
mathematics of various entertaining subjects. Vol. 3
Princeton University Press, Princeton, NJ, 2019.
Allie Wicklund, "A
sexage, densitydependent matrix model for whitetailed deer
populations incorporating annual harvest", preprint (2016)
Tyler
George, "Eergodicity
and speedups of ergodic systems" RoseHulman
Undergraduate Math. J. 16
(2015) 7287.
Keith
Goldner, "A Markov
model of football" J.
Quant. Anal. Sports 8
(2012) (online, 16 pp.)
