Ten years ago today (8/14/2003), the northeastern U.S. suffered the worst blackout in U.S. history, when about 15 million people lost power. The massive loss of power was attributed to a small event that cascaded through the complex power distribution system.
This raises the more general question of systemic risk in complex systems – a topic about which mathematics has much to say. The issue is not limited to the power grid, although that too is very much in the news today. Other complex systems including ecological systems, banking systems and large engineered systems can also exhibit cascading failures through interconnected components.
What can mathematics say about systemic risk in such complex networks? There are a number of resources on this topic. A talk by George Papanicolaou, which focused primarily on risk in the financial sector, may be heard (audio synchronized to viewgraphs) on line. An article by James Case (SIAM News, December 2013) also covered this talk.
Furthermore, the U.S. National Academy of Sciences’ Board on Mathematical Sciences and its Applications issued a report in 2007 that addresses many of these issues as well.
The area of systemic risk remains an active field of research in mathematics and statistics, with many interesting and difficult problems. Some of these are touched upon in the above references.
With further research one hopes to avoid being kept in the dark by a small event that magnifies as it propagates through a complex system.
And then there is the banking system….