Algebraic $K$-Theory and Motivic Cohomology

Abstract

Algebraic $K$-theory and the related motivic cohomology are a systematic way of producing invariants for algebraic or geometric structures. Its definition and methods are taken from algebraic topology, but it has also proved particularly fruitful for problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of results on $K$-theory itself and applications. We had a lively evening session trading questions and discussing open problems.