The primary goal of ACMS is to provide an environment for research and learning in the Mathematical Sciences. Its basic research themes are the modeling, understanding and applicability of nonlinear processes in optics, fluids, neural networks, and random distributed systems with continuing investigations into pattern dynamics, percolation, behavior of lattice gasses, nonlinear stability, low dimensional chaos, turbulence, dynamical systems and the nature of integrable systems of differential equations.

Research and learning takes place at all levels. The breadth of activity and spectrum of interest and talent among visiting collegaues serves to stimulate interdisciplinary work and promote the cross fertilization of ideas. Graduate students interested in applied mathematics enjoy a unique environment in which they can experience first hand the unity in the approaches (modeling, simulation, analysis, and involvement in experiments) with which mathematical scientists tackle a diverse set of problems from all areas of the physical sciences. There are several ongoing weekly working seminars in addition to regular departmental colloquia. These are in the areas of applied analysis, computation, dynamical systems, nonlinear optics, neural networks, integrable systems, and mathematical physics.

Nonlinear Optics has attained a special status at ACMS and the exceptional multidisciplinary culture at Arizona provides a unique environment for collaborative research with colleagues at the Optical Sciences Center, and the Program in Applied Mathematics. Graduate students in Applied Mathematics, Optical Sciences and Physics work together on research projects at the frontiers of this exciting field. Tucson's designation as "Optics Valley", reflects the large concentration of Optics industries in the region and provides a strong industrial link to the University of Arizona.