Key notions from statistical physics, such as "phase transitions" and "critical phenomena," are providing important insights in fields ranging from computer science to probability theory to epidemiology. Underlying many of the advances is the study of phase transitions on models of networks. Starting from the classic ideas of Erdos and Renyi, recent attempts to control and manipulate the nature of the phase transition in network connectivity will be discussed. Next, the influence of self-organization on phase transitions will be presented, as well as connections between the jamming transition in models of granular materials and constraint satisfaction problems in computer science. Finally, turning to network growth, I will show that local optimization can play a fundamental role leading to the mechanism of Preferential Attachment, which previously had been assumed as a basic axiom and, furthermore, resolves a long standing controversy between Herb Simon and Benoit Mandelbrot.

Speaker Bio:

Raissa D'Souza is a faculty member in the Center for Computational Science and Engineering, and the Mechanical Engineering Department at UC Davis, as well as an external professor at the Santa Fe Institute. She received a PhD in statistical physics from MIT in 1999, then was a postdoctoral researcher at Bell Laboratories and at Microsoft Research. She has been a short-term visiting scientist at Caltech, MSRI, IPAM, The Santa Fe Institute and ENS in Lyon France. Raissa's research focuses on self-organization and growth in both natural and engineered systems and her current work and publications span the fields of physics, computer science and applied math.