Complex Systems and Network Science
Some of the most fascinating problems in applied mathematics today concern the structure and dynamics of systems composed of many interacting parts. Think of the thousands of power plants in the electricity grid or the companies in global economy; the billions of people on Facebook; or the hundreds of billions of neurons in the human brain. In each of these complex systems, the individual parts interact with a subset of the others, and the pattern of connections between them defines a network. Faculty and students at CAM are using the tools of graph theory, statistical physics, machine learning, probability theory, and dynamical systems to look into the complex architecture and collective behavior of the diverse networked systems in the world around us.