When the mathematician Andrea Bertozzi started her new job at the University of California, Los Angeles, in 2003 she decided to use her skills to study a problem that has plagued LA for a long time: crime.
Crime is a problem in most cities, but as we all know, not all neighbourhoods are affected in the same way. There are crime hotspots you wouldn't want to enter alone on a dark night, or even during the day. It's clear that all sorts of factors contribute to turning an area into one of those: for example its socio-economic standing, or the density of the population. It would be useful to get a clearer understanding of the dynamics of hotspots. This is where maths can help. You can try to describe the processes involved using mathematical rules and equations — build a mathematical model — and see what this simplified version of reality tells you about what's going on.