The Annual William Marshall Bullitt Lecture
|2014 BULLITT LECTURE
Using Mathematics to Understand Territories
Dr. Mark Lewis
Centre for Mathematical Biology
University of Alberta
March 20th, 2014
University of Louisville
Abstract: Mathematical models
can help us understand the formation of complex spatial patterns, including
the formation of territories. In wolves and coyotes scent marks provide
important cues regarding the use of space. In this talk I will show how
biologically-based mechanistic rules can be put into a mathematical model
which predicts the process of territorial formation as individuals create
and respond to scent marks. The model predicts complex spatial patterns
which are seen in nature, such stable "buffer zones" between territories
which act as refuges for prey such as deer. The mathematical work is supported
by detailed radio-tracking studies of animals. I will also employ the approach
of game theory, where each pack attempts to maximize its fitness by increasing
intake of prey (deer) and while decreasing interactions with hostile neighboring
packs. Here the predictions are compared with radio-tracking data for wolves
and coyotes. Finally I will show how a version of the territorial model
has been applied to human populations in understanding spatial patterns arising
from conflict between urban gangs.
OPEN TO THE PUBLIC
for more information, contact firstname.lastname@example.org
or call (502) 852-6826
(click on image to download
PDF of the poster)
is also a Bullitt Lecture
The Mathematics Department’s
Bullitt Lecture is a free, public lecture that has brought to Louisville
each year, beginning in 1993, a distinguished mathematician to speak to 200-500
audience members about important and cutting-edge mathematics. Ronald Graham,
former Chief Scientist at AT&T, and Indiana University College Professor
of Cognitive Science and Computer Science, author and computer scientist Douglas
R. Hofstadter (author of Gödel, Escher, Bach) are former Bullitt Lecturers.
The emphasis has been drawing people from the outside academia. Talented
high school students, area professionals, and other parties interested in
the impact and excitement that mathematics has generated, especially in the
last decade, have attended the Bullitt Lecture in surprisingly large numbers.
is endowed through a grant from the family of William Marshall Bullitt, the
Solicitor General of the United Stated under President William Howard Taft.
first Bullitt lecture was given by Jerry King of Lehigh University (a native Kentuckian, UK
Ph.D) on the
subject of his then popular book "The Art of Mathematics," Plenum Press, NY and London, 1992.
It took place on April 5, 1993.
lecture was given by Professor Fred Rickey, one of the leading American historians of mathematics
who was then at Bowling Green University (and is now at the United States
Military Academy at West Point), on the then popular topic of the history
of Fermat's Last Theorem. Recall that Andrew Wiles had announced
his proof of
FLT in the summer of 1993. Professor Rickey's talk took place in April
gave the third lecture in 1995 on visualizing the 4th dimension. After 1995,
the Bullitt Lecture was advertised via posters shown below.
on photo to download PDF file containing the poster.
(some of these files are large, > 1mb)
Bullitt, the Solicitor General of the United Stated under President William
Howard Taft, was a Louisville native and an 1894 Princeton graduate. He
received his law degree from the University of Louisville. Bullitt is descended
from one of the most prominent Kentucky families- five Kentucky counties
bear the name of his direct ancestors.
an authority on insurance law and wrote a number of important pamphlets in
actuarial mathematics. He was a personal friend of a number of important
figures in twentieth-century mathematics, including G.D. Birkhoff, G.H. Hardy,
and Albert Einstein.
family had already compiled collections of rare books in history, horticulture,
and other field when William Marshall Bullitt decided to pursue acquisitions
of rare mathematical editions. Bullitt began by seeking the aid of mathematicians
and historians of mathematics in determining a list of ``25 Greatest Mathematicians
(Excluding all Living Mathematicians)”. Prior to World War II, Bullitt and
his wife traveled extensively in Europe; his cousin, William Christian Bullitt,
was the American Ambassador to France at the time. Bullitt put together
a magnificent collection of rare and significant mathematics. “Strangely
enough, anyone wishing to write about Galois in Paris would do well to journey
to Louisville, Kentucky,” wrote Leopold Infeld, author of Whom the Gods Love,
a fictionalized biography of the celebrated French mathematician Evariste
Galois. A well-written account of Bullitt and his efforts to obtain rare
mathematics manuscripts is given in ``William Marshall Bullitt and His Amazing
Mathematical Collection”, by Richard M. Davitt (Professor of Mathematics
at the University of Louisville), in The Mathematical Intelligencer, Vol.
11, No. 4, 1989.
Bullitt’s wife gave the entire mathematics collection and related correspondence
to the University of Louisville, where today it is the William Marshall Bullitt
Mathematical Collection. Visitors from around the world visit the Collection.
Members of the Bullitt family are frequent Lecture attendees. The mathematics
community—indeed, the entire Louisville community—gratefully and gladly acknowledges
the debt to the family for the inestimable contribution