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Explore the fundamental concepts of ergodicity in smooth dynamics through this comprehensive lecture. Delve into the intricacies of smooth systems, examining various examples and proofs. Gain insights into higher dimensions and homomorphisms as speakers Jana Rodriguez-Hertz and Amie Wilkinson guide you through this advanced topic. Learn about the relationship between mathematics and ergodicity, and understand its applications in dynamic systems. Engage with a structured syllabus that covers introduction, countries, personal mathematical relationships, smooth systems, examples, proofs, higher dimensions, homomorphisms, and concludes with a summary and final example.