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タイトル Baum-Connes Conjecture and Direct Splitting Method 2018年6月15日 13：00～14：30 Shintaro Nishikawa 氏（Penn State University） 矢上キャンパス14-631A/B（14棟6階ミーティング1A/B） For a group $G$, the Baum-Connes Conjecture (Baum and Connes, 1982) states that the assembly map, a mysterious map going from the left-hand (topological) side to the right-hand (algebraic) side, provides an isomorphism (of abelian groups) between K-homology of $G$-spaces and K-theory of the reduced group C*-algebra of $G$. Starting with an introduction to this conjecture for general audiences, I will introduce and explain our new method for studying the Baum-Connes Conjecture, which we call Direct Splitting Method. This is a method of directly producing a candidate of a potential inverse of the Baum-Connes assembly map. This method can simplify and clarify proofs of some of the known cases of the conjecture. This work is related to my recent work with J. Brodzki, E. Guentner and N. Higson.