Applying Categorical Thinking to Practical Domains - From Probabilistic Modeling to Robotics

Explore a comprehensive colloquium talk that demonstrates how categorical thinking can be effectively applied across diverse practical domains, focusing on probabilistic modeling, hierarchical clustering, and robotics. Delve into the formalization of behavior application in legged robots with hybrid dynamical system controllers, examining three key aspects: sequential composition of hybrid systems through cospan descriptions and Conley's (epsilon,T)-chains, hybrid system transformations via semiconjugacies within a double category framework, and hierarchical composition using hybrid subdivisions with template/anchor pairs. Learn from practical lessons gained through implementing categorical formalisms in real-world scenarios, gaining insights into how mathematical abstractions can enhance understanding and problem-solving across multiple disciplines.