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The last few years have witnessed an explosion of progress in algebraic K-theory. Derived algebraic geometry and non-commutative methods have been refined into powerful tools, especially through the theory of localizing invariants. Trace methods have brought K-theory and topological cyclic homology closer together than ever before. Perfectoid techniques mean that K-theory benefits from the recent progress in p-adic cohomology, such as prismatic cohomology. Condensed mathematics provides at long last a uniform approach to the K-theory of topological rings. Geometric foundations for motivic stable homotopy theory have been laid and new motivic filtrations have been unearthed.

The goal of the Summer School will be to help bring the participants up to date on these exciting developments, via research lectures, mini-courses, and an Arbeitsgemeinschaft on the topic of syntomic and étale motivic cohomology.