This three-year, $345,394 National Science Foundation Project Grant supports research into the topology of three-dimensional spaces through the study of veering triangulations and their relationship to possible flows through such spaces. Specifically, the principal investigator and collaborators aim to prove that veering triangulations correspond to pseudo-Anosov flows, produce new Cannon-Thurston maps using these triangulations, and establish connectivity properties for triangulations in higher dimensions. Additional goals include extending the existing census of veering triangulations and developing virtual and augmented reality experiences to aid in research, pedagogy, and outreach related to Thurston and other geometries. Oklahoma State University will utilize the funding to advance these mathematical investigations and further the National Science Foundation's mission under the Mathematical and Physical Sciences program (CFDA 47.049) to strengthen the nation's scientific enterprise through increasing knowledge and understanding of major problems.