The Gomez research group works to understand how charged defects alter ionic conduction pathways in materials. Currently, we have focused on two key materials: doped perovskite oxides with technological applications to proton conduction in fuel cells and lithium/lanthanum/zirconium oxides with applications to lithium-ion conduction in batteries. The team uses ab initio tools to generate data sets of minima and transition states to create maps or graphs for ionic conduction in the presence of charged defects. The large graphs are then searched by both traditional graph theory tools and team developed extensions.