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This lecture by Maani Ghaffari, Assistant Professor at the University of Michigan, explores how computational symmetry and learning can advance robotics capabilities. Discover how mobile robots can be designed to operate autonomously in challenging environments through efficient, generalizable algorithms. Learn about the current limitations in robotics despite recent advances, as no robot yet matches human-level performance in everyday tasks like search and rescue, exploration, and environmental monitoring. Follow along as Ghaffari explains the structures that emerge when combining symmetry, geometry, and learning in fundamental robotics problems, with experimental demonstrations spanning from perception to control. The presentation concludes with insights on promising future directions based on both field and academic experiences. Presented at Georgia Tech's Klaus Computing Building on March 5, 2025.