Departmental Colloquium on 2nd November 2017 at 4:00 pm Blackett Lecture Theatre 112

Professor Ian Stewart, Emeritus Mathematics Professor, University of Warwick and a Fellow of the Royal Society  

Networks, Singularities, and Homeostasis

Abstract: Homeostasis occurs in a biological or chemical system when some output variable remains approximately constant as an input parameter varies over some interval. I will discuss joint work with Martin Golubitsky, Mike Reed, Janet Best, and Fred Nijhout on how to find homeostasis intervals. Multivariable generalisations are also possible. We reformulate homeostasis in the context of singularity theory, by replacing approximately constant by the output has zero derivative with respect to the input. We use analytic or numerical methods to find such points. Unfolding theory then classifies all small perturbations of the input-output function. For the `chair' singularity, which is especially important in applications, the normal form of the universal unfolding is x3 + ax. Examples from and applications to biology will be described, probably including thermoregulation in opossums, feed-forward inhibition in biochemical networks, and motifs in gene regulatory networks of organisms such as E. coli and yeast​.

Bio: Ian Stewart is an emeritus mathematics professor at the University of Warwick and a Fellow of the Royal Society. He is author or coauthor of over 180 published research papers on pattern formation, chaos, network dynamics, and biomathematics. He has published over 100 books including Does God Play Dice?, Nature’s Numbers, Why Beauty is Truth, Professor Stewart’s Cabinet of Mathematical Curiosities, 17 Equations that Changed the World, Infinity, Calculating the Cosmos, and the four books of the bestselling Science of Discworld series with Terry Pratchett and Jack Cohen. He has also published five science fiction novels: Jack of All Trades; Wheelers and Heaven with Jack Cohen; The Living Labyrinth and Rock Star with Tim Poston. He has five honorary degrees, and his awards include the Royal Society’s Faraday Medal, the IMA Gold Medal, the AAAS Public Understanding of Science Award, the LMS/IMA Zeeman Medal, the Lewis Thomas Prize, and the Euler Book Prize. He is an honorary wizard of Unseen University on Discworld.