Explore the intersection of geometry and legal studies in this illuminating lecture on Supreme Court voting behavior. Delve into the field of empirical legal studies and discover how data analysis is shedding new light on the U.S. court system. Learn about recent investigations that apply planar geometry and phylogenetic trees to understand the decision-making processes of Supreme Court judges. Gain insights into the potential for further research combining topology and geometry with legal analysis. Examine the context of key problems in this field and consider innovative approaches to studying influential judicial decisions. Uncover the power of interdisciplinary research as mathematics meets political science in this fascinating exploration of the highest court in the United States.