This volume consists of selected contributions from the ""Georgia Institute of Technology-UAB International Conference on Differential Equations and Mathematical Physics"". The book offers a combination of certain emerging topics and important research advances in this active area. The topics range widely and include magnetic Schrodinger operators, the Boltzmann equations, nonlinear variational problems, and noncommutative probability theory. Some articles were included for their aesthetic value and others to present an overview. All articles were reviewed for scientific content and readability. The text is suitable for graduate and advanced graduate courses and seminars on the topic.