Download Report

The
In Memory of
Nathan Altshiller Court
(1881–1968)
Oklahoma-Arkansas Section
proudly presents
N.A. Court was a Polish Jew turned American who is one of the
great local intellectual pioneers of the 20th century. Most of his
professional life was spent at the University of Oklahoma from
his hiring in 1916 until his retirement in 1951. He spent those
years doing the things he loved most: teaching university students, spreading his love of mathematics by writing three textbooks and a voluminous collection of research articles, sharing
his love of languages and life, and being a beloved and legendary
member of society. He holds a unique place in the mathematical history of the Oklahoma-Arkansas geographical area. It is
for these reasons that the Section honors him annually with the
Lecture that carries his name.
the
43rd N.A. Court Lecture
Friday, 10 April 2015 at 19:45
Gilcrease Museum, Vista Room
For a biography of Dr. N.A. Court and a list of past N.A. Court
lecturers, please go to http://sections.maa.org/okar/ and access
the History section.
Tulsa, Oklahoma
N.A. Court Committee:
Scott McClendon, Chair
Nick Zoller
Ramesh Garimella
Sponsored by
Oklahoma-Arkansas Court Endowment Fund
Competitive Exclusion and Coexistence in Population
Models
The Lecturer
Dr. Azmy S. Ackleh
Louisiana State University at Lafayette
Azmy S. Ackleh received his Ph.D. from the University of
Tennessee at Knoxville in 1993 under the supervision of Thomas
G. Hallam. He then joined the Center for Research in Scientific
Computation at North Carolina State University as a postdoctoral fellow until 1995 where he became an Assistant Professor
of Mathematics at the University of Louisiana at Lafayette. In
2000 he became an Associate Professor of Mathematics and in
2003 he became a Full Professor of Mathematics. In 2007 he
was selected to become the R.P. Authement Eminent Scholar
and Endowed Chair in Computational Mathematics at the University of Louisiana at Lafayette. In 2011 he became the Department head of Mathematics and in 2013 he became the Dean
of the R.P. Authement College of Sciences at the University of
Louisiana at Lafayette.
Competitive interactions between organisms play a significant role in structuring ecological communities. These interactions occur when two or more species rely on the same basic living resources that are in short supply. The question of
when do competing species coexist and when do they exclude
each other has long intrigued both ecologists and mathematicians. In 1932 Gause formulated the well-known Competitive
Exclusion Principle which states that two species competing for
the same resources cannot coexist if other ecological factors are
constant. Thereafter, experiments and mathematical models
(beginning with the Lotka-Volterra model) have been used to
support or violate this tenet. In this talk, several population
models will be presented and conditions under which competitive exclusion occurs and conditions under which coexistence is
possible will be established. A particular focus will be on a general class of selection-mutation models formulated on the space
of finite signed measures. This class of models assumes that the
trait space is either continuous or discrete and that competition occurs between individuals with different traits. It is then
demonstrated that under pure-selection dynamics the solution
converges to a Dirac measure centered at the fittest trait. It is
also shown that when the trait space is discrete, the selectionmutation model with small mutation has a locally asymptotically stable equilibrium that attracts all initial conditions that
are positive at the fittest trait.
Ackleh’s research is in the area of Mathematical Biology. He
published more than 120 peer-reviewed articles in this area and
one graduate level textbook. He is particularly interested in the
development of continuous and discrete models in population
ecology and epidemiology and in using mathematical tools to
understand the short-term and long-term behavior of solutions
to these models. He develops numerical methods for solving nonlinear PDEs arising in such applications, and uses these numerical schemes to analyze the solution behavior. He also applies
functional analysis and dynamical systems approaches to study
stability and persistence properties of populations. Particular
applications that he has worked on include selection-mutation
models, amphibian dynamics, the interaction between blue and
yellow irises, and the impact of oil spills on marine mammals
in the Gulf of Mexico. He directed the dissertations of twelve
Ph.D. students and received more than $8M in external funding
from several agencies including, NSF, NIH and GoMRI (Gulf of
Mexico Research Initiative).
********************
********************
Did you know?
Nathan Altshiller became a naturalized citizen of the United States of
America in 1919. Concerned about his German-sounding last name, he
changed Altshiller to his middle name and adopted the new last name
Court. He did so in appreciation of the American Court of Justice.
Did you know?
N.A. Court spoke seven languages: Russian, Polish, Hebrew, French, German, English, and Italian