Explore transverse groups, also known as antipodal regular groups, in this comprehensive lecture by Andrew Zimmer from the University of Wisconsin, Madison. Delve into the discrete group class that encompasses Anosov and relatively Anosov groups. Discover the metric and flow space on which these groups act, drawing parallels to the Cayley graph and geodesic flow space of word hyperbolic groups. Learn about new research findings derived from these spaces, presented as part of a collaborative effort with Richard Canary and Tengren Zhang. Gain insights into advanced mathematical concepts and their applications in this hour-long talk delivered at the Institut des Hautes Etudes Scientifiques (IHES).