Various problems arising in games and sports will be analyzed mathematically. For example how many shuffles are needed to mix a deck? How should a runner vary his speed for minimal time? When is a team eliminated from winning the pennant? How should we rank teams in a league? Does exercise affect life span? These and other problems will be considered.
Network structures are pervasive in the natural and engineered world, from biological networks, to social networks, to the Internet. In recent years we have seen an explosion of work laying the foundation for a mathematical "science of networks". This talk will survey some existing networks and discuss recent advances in understanding network growth, phase transitions on models of networks and applications to systems such as self-organizing sensor networks, world-wide-web search engines, and traffic flow.