Ambidexterity in Topology and Algebra - Lecture 4

Explore the concept of ambidexterity in a lecture from the "Dualities in Topology and Algebra" program. Delve into advanced topics in algebraic topology, commutative algebra, and modular representation theory of finite groups. Examine duality phenomena and classification problems in tensor-triangulated categories. Investigate connections between derived categories of commutative rings, stable categories of finite groups, and stable homotopy categories in topology. Learn about Grothendieck duality theory, Gorenstein rings and schemes, and their applications to generalizations of Poincaré duality for manifolds. Discover the classification of thick and localising subcategories of triangulated categories and the computation of their spectra. Gain insights into cohomological support varieties and their development in modular representation theory. Enhance your understanding of these complex mathematical concepts through expert explanations and discussions.