I²CNER has begun exploratory projects that are situated precisely at the intersection of applied math and engineering because we believe this area has enormous potential to impact all of the Institute’s research areas and the general scientific community. In general, I²CNER’s Applied Math initiatives are aimed at integrating the vast numberof energy pathways into the energy infrastructure from various perspectives, such as analysis, compatibility, and optimization,among other things. Since we are interested in both basic science and engineering perspectives of energy pathways, we are also exploring new investigative techniques. The Institute currently has ongoing projects on modeling the smart electric grid based upon a thorough understanding of how energy generation, demand, and storage interact with the electric grid, especially in the residential energy sector, and using persistent homology to characterize the properties of porous materials,which is critically important for CO2 storage in rock formations. Our foremost aim in these initiatives is to explore high-priority, high-rewardareas that will inform the future research directions of I²CNER in the general area of applied math for energy.