Problems in the Physical and Engineering Sciences have always provided a strong motivation for the development of many branches of Mathematical Analysis. For instance efforts to describe the motions of the planets led to the birth of Calculus and to the Theory of Differential Equations. Problems of Civil Engineering and Cartography gave rise to the Calculus of Variations and Differential Geometry. The needs of modern science continue to spur the development of analytical methods. The Department of Mathematics at the University of Arizona places a strong value on research that is both scientifically relevant and mathematically novel. The first and still most recognized journal of Nonlinear Science, Physica D, was founded in our Department. Today faculty are actively involved in research programs that address emerging theoretical needs in Microbiology, Materials Science, Photonics, Quantum Field Theory, Complex Fluids and Condensed Matter Physics. Our group organizes a weekly seminar to discuss new developments.