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Explore the intricacies of algebraic and topological K-theory in this comprehensive lecture by Andreas Thom, part of the Hausdorff Trimester Program on Applied and Computational Algebraic Topology. Begin with a general introduction to K-theory and its fundamental applications in algebra, geometry, and number theory. Delve into the comparison between algebraic and topological K-theory for specific rings of functional analytic type, with a focus on the algebraic K-theory of stable algebras and rings of continuous functions. Gain insights into homotopy invariance theorems for algebraic K-theory stabilized by suitable operator ideals and negative algebraic K-theory of rings of continuous functions, time permitting.
