I2CNER’s research at the intersection of applied math and engineering has enormous potential to impact all of the Institute’s research areas and the overall energy challenge. I2CNER’s applied math efforts are aimed at integrating the vast number of energy pathways into the energy infrastructure from various perspectives such as analysis, compatibility, and optimization. The Institute currently has ongoing projects in the areas of the mathematics of smart grid, porous materials, computational physics, and biomathematics. Examples include algorithm development for scalable grid optimization problems, study of strategic interactions in electricity markets by accounting for the deepening penetration of variable renewable resources in the grid, and persistent homology to characterize the properties of porous materials for CO2 storage in rock formations. Projects are also addressing efficiency increase in power generation by modeling expanding flames through using theory of parabolic equations, and they are deploying biomathematics for the study of growth rates in feedstock plants for renewable energy.