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Explore the connections between Davis-Lück homology and Weibel's homotopy K-theory through the lens of equivariant algebraic kk-theory in this 44-minute lecture. Delve into the application of homotopy theory and adjointness theorems to establish these relationships. Gain insights into the assembly map for the KH-isomorphism conjecture introduced by Bartels-Lück, with a focus on expressing its left-hand side using equivariant algebraic kk-groups. Presented by Eugenia Ellis from Universidad de la República, this talk offers a deep dive into advanced topics in algebraic K-theory and its applications.