Explore the intricacies of quantum phases of matter in this comprehensive lecture focusing on non-perturbative Luttinger relations. Delve into the Anderson Lattice Model and Kondo Lattice model, examining their key concepts and applications. Gain insights through practical examples and a detailed conclusion on the Kondo lattice model. Analyze Oshikavan's non-perturbative argument, including its assumptions and implications. Investigate the coupling of spin gauge fields and engage with the speaker's arguments and conclusions. Participate in a thought-provoking Q&A session to further enhance understanding of these complex quantum phenomena.