Mathematics and physics have interacted fruitfully for centuries. Physics has been a constant source of interesting mathematical problems, and these problems have often required new mathematics for their solution. Conversely, advances in mathematics have found surprising and impressive applications in physics.

Research in mathematical physics at the University of Arizona centers around the areas of classical and quantum statistical mechanics, quantum field theory, and random or disordered systems. Some specific topics include spin glasses, quantum electronic systems, solvable models, percolation, random matrices, and localization. The mathematics involved in this research comes from analysis, probability and geometry.