Dr. Karen Ames Lecture Series on Applied Mathematics Dr. Brian Straughan Durham University, United Kingdom April 13, 2007202 Madison Hall3:00 PM (Refreshments at 2:30 in 201 Madison Hall) Abstract We study a model for aggregation, in space, of microglia. Using biological parameters found in the literature, testable thresholds are derived such that aggregation will not form if conditions are less than the threshold. This yields criteria which may determine usable bounds under which Alzheimer's disease senile plaques cannot form. The model we use has been developed by Luca et al. (2003) and involves chemoattractant and chemorepellent chemicals. Our analysis applies to two and three dimensional spatial domains. Biographical Sketch Dr. Brian Straughan was Simson Professor of Mathematics in the University of Glasgow from 1991 - 2000 and is now Professor of Numerical Analysis in Durham University. Among his achievements he was elected a Fellow of the Royal Society of Edinburgh, 1986, awarded a Max Planck Research Prize by the Alexander von Humboldt Foundation, in 1994, and elected a Foreign Member of the Accademia di Scienze, Fisiche e Matematiche di Napoli, 1995. He has published many research books, including one with Dr. Karen A. Ames, and research papers, including those also with Dr. Karen A. Ames.