Explore a comprehensive lecture on Feynman's approach to constructing commuting higher Hamiltonians for Calogero models, presented from a contemporary viewpoint. Delve into the intricate mathematical foundations and physical implications of these models as explained by speaker Yehao Zhou. Gain insights into the historical context of Feynman's work and its relevance to modern physics. Examine the mathematical techniques and physical principles employed in the construction of these complex systems. Analyze the significance of commuting higher Hamiltonians in the study of integrable systems and their applications in theoretical physics. Enhance your understanding of advanced concepts in mathematical physics and quantum mechanics through this in-depth, 71-minute presentation at the Galileo Galilei Institute.