Conference on Waves and Continuation Methods in Biology and Related Areas

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Hastings 9801227 The investigator and his colleagues organize an interdisciplinary conference to bring together biologists and mathematicians to discuss wave phenomena from their varying perspectives. The conference aims to give both biologists and mathematicians insights into the types of models that can be used for wave phenomena and the parameter ranges where such behavior can be expected. To this end, the conference includes both general lectures and more technical talks where particular techniques are explored more fully. Of special interest in techniques are continuation methods in models of long range interaction, where integral equation models are involved. One-dimensional traveling waves have long been of interest to biologists, particularly in neurobiology where they describe the propopagation of electrical signals down a nerve axon or as a plane wave across a two-dimensional collection of electrically active cells. Related phenomena include spiral and other patterns, such as those thought to be responsible for some pathogenic behavior in cardiac tissue. Similar patterns in the brain are of current interest as well. Such behavior is not limited to neurobiology, and appears in a wide variety of chemical and biological systems, such as the Belousov-Zhabotinsky reaction, slime molds, and many others. On the other hand, mathematicians have studied basic questions about waves for a variety of models, including biological and chemical settings. One focus of mathematical work has been to prove the existence and stability of traveling waves. In this regard continuation methods have become particularly interesting in models of long range interaction, where integral equations are involved. The conference brings together biologists and mathematicians to discuss wave phenomena from their different perspectives. The meeting fosters interactions between the two areas that should lead to greater understanding of a variety of phenomena important in biology.