Analog and Universal Complexity in Robotics and Manifolds

Explore the concept of analog complexity and its implications in robotics and computational theory in this thought-provoking lecture. Delve into a reinterpretation of Smale's seminal paper, examining the trade-offs between digital and analog approaches in robotic systems with access to randomness. Investigate the notion of "analog category" and its surprising properties for finite groups, drawing parallels to the Eilenberg-Ganea theorem. Gain insights into the development of universal parametrised complexity for certain manifolds, and discover how these concepts intersect with broader themes in applied algebraic topology. Engage with cutting-edge research that bridges the gap between theoretical foundations and practical applications in robotics and computational complexity.