Delve into the fourth lecture of a series on Duality and Stratification in Commutative Algebra, presented by Srikanth B. Iyengar at the International Centre for Theoretical Sciences. Explore advanced concepts in algebraic topology, commutative algebra, and modular representation theory of finite groups during this 1 hour and 24 minute session. Gain insights into the derived category of commutative rings, Grothendieck duality theory, and Gorenstein rings and schemes. Examine the classification of thick and localising subcategories of triangulated categories, and discover how ideas from algebraic topology and abstract homotopy theory have influenced algebra and geometry. Enhance your understanding of cohomological support varieties and their applications in modular representation theory. Suitable for those with a background in algebraic topology, commutative algebra, and homological algebra, this lecture is part of a comprehensive workshop bringing together experts to explore duality phenomena and classification problems in tensor-triangulated categories. Read more