Explore the third lecture in a series on Quillen's Stratification Theorem(s) delivered by Natalia Castellana as part of the "Dualities in Topology and Algebra" program. Delve into advanced concepts in algebraic topology, commutative algebra, and modular representation theory of finite groups. Examine the connections between these mathematical fields, focusing on duality phenomena and classification problems in tensor-triangulated categories. Gain insights into the derived category of commutative rings and its relationship to stable categories in group theory and topology. Investigate Grothendieck duality theory, Gorenstein rings, and their applications in algebraic topology. Learn about the classification of thick and localising subcategories in triangulated categories and explore cohomological support varieties. Enhance your understanding of these complex mathematical topics through expert instruction and discussion sessions.