The production, distribution, storage, and use of electrical energy are undergoing significant changes. Demand and production patterns are being altered radically by the advent of “smart grids,” renewable generation, hybrid electric vehicles and storage technologies, and by new regulatory constraints. The uncertainties and challenges such as discrete nature, dynamics, and multiple scales—raise a critical need in the energy sector for new mathematical and computational tools. The M2AC2S Center is a locus for a multifaceted, integrated applied mathematics program for the DOE grand challenge of complex electrical energy systems and related infrastructure. Motivated by the applications to complex energy systems, we perform leading-edge research in fundamental mathematical challenges in predictive modeling, integrative mathematical analysis and abstraction frameworks, mathematics of decision, and scalable algorithms. We aim to make integrated advances across these areas and bring them to bear on subchallenges in complex electrical energy systems and related infrastructure: integrated grid and infrastructure planning under sustainability considerations; next-generation architectures for electricity generation, storage and distribution; real-time interconnect-wide system model calibration and prediction; and predictive control of cascading blackouts and real-time contingency analysis. The research program intends to foster integration of mathematical techniques and cross-fertilization across math disciplines.