Ambidexterity I by Neil Strickland

Explore the concept of ambidexterity in mathematics through this lecture by Neil Strickland, part of the "Dualities in Topology and Algebra" program at the International Centre for Theoretical Sciences. Delve into the connections between algebraic topology, commutative algebra, and modular representation theory of finite groups, focusing on duality phenomena and classification problems in tensor-triangulated categories. Gain insights into derived categories, stable homotopy categories, and their similarities and differences. Examine how ideas from commutative algebra and algebraic geometry have been applied to modular representation theory and stable homotopy theory, including Grothendieck duality theory and Gorenstein rings. Discover the classification of thick and localising subcategories of triangulated categories and the computation of their spectra. Suitable for those with a background in algebraic topology, commutative algebra, and homological algebra.