Background
What do the human genome, the Internet, the propagation of HIV infection and financial markets have in common? At first glimpse one would say nothing. However, at a different level of abstraction, one would recognize a similar network-structure in the interactions between their constituting elements. More generally, they are complex systems, in the sense that they involve a very large number of constituents whose interactions lead to behaviors that cannot be predicted by simply understanding the behaviors of the constituents parts. In science, complexity emerges in many different systems and domains. In recent years modern technology has allowed us to gather, store and process huge amounts of data for each of these systems making -for the first time- detailed empirical studies doable. From these studies several common features have emerged and many theoretical and numerical tools have been developed.
A few years ago, Stephen Hawking was predicting that “the next century will be the century of complexity”. Indeed, science (and physics in particular) is changing in response to the new challenging problems arising from the science of complex systems. The last decade has seen a great deal of new methodologies being invented, and a host of new paradigms being tested.

Course Topic and Contents
This course intends to introduce novel theories and paradigms developed in recent years to study complex systems. The students will be exposed to a range of topics with special focus on the theory of extreme events, collective dynamics of highly correlated systems, self organization, cascade events, applications of network theory and statistical mechanics. See Lectures.