Explore the second lecture 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. Investigate the derived category of commutative rings and its relation to stable categories in group theory and topology. Learn about Grothendieck duality theory, Gorenstein rings, and their applications in algebraic topology. Discover how ideas from algebraic topology and abstract homotopy theory have influenced algebra and geometry. Study the classification of thick and localising subcategories in triangulated categories and explore Balmer's notion of spectra. Gain insights into cohomological support varieties and their development in modular representation theory. Enhance your understanding of these advanced topics through complementary background lectures and discussion sessions. Read more