MSI Weekly Bulletin - Week starting Monday 12 December, 2005

I will present four examples, from my own and other's work, to demonstrate that mathematics is useful and essential for understanding complex systems, both closed and open: 1) Adding new road capacity can increase travel time for everyone; 2) Self-sustaining clusters can emerge even when it appears death rate exceeds reproduction; 3) Everlasting self-localised excitations can occur even when linear theory would suggest they would radiate away, and media which are insulating for linear theory can be conducting nonlinerarly; 4) Indecomposable spatially extended deterministic systems (as well as stochastic ones) can exhibit non-unique probabilistic behaviour and sensitivity to boundary conditions. http://wwwrsphysse.anu.edu.au/ccs/seminarAbstracts.php#MacKay05_1