Groupoid homology and C*-algebras (Lecture III)

Valerio Proietti  (University of Oslo)

15:30-17:00,October 27, 2025    普陀校区 理科大楼A503

Abstract:

This is Lecture 3 of the lecture series. This lecture will explain how groupoid homology can be used to answer questions regarding classifiable C*-algebras and their K-theory. For simplicity, I will focus on the case of ample groupoids and consider in particular C*-algebras attached to topological dynamical systems. I will sketch the proof/refutation of two conjectures: (1) K-theory groups of Smale space C*-algebras have finite rank; (2) The range of K-theory on the class of classifiable real-rank-zero C*-algebras is exhausted by C*-algebras of Smale spaces. I will start with an overview lecture providing motivation and outlining the overall strategy, and continue by introducing the essentials of groupoid homology and its relation with K-theory (2 lectures), and finally explaining a streamlined proof/refutation of the problems above.

About the speaker:

Valerio Proietti 是一位活跃的青年学者，研究兴趣涵盖 K 理论、群胚同调、动力系统、指标理论及量子群等。他在群胚的 Baum-Connes 猜测与同调论方面取得了重要成果，包括与Yamashita 建立了群胚同调的新模型，揭示了 Matui 的 HK 猜测与群胚 Baum-Connes 猜测之间的联系，并解决了 Putnam 及 Putnam-Kaminker-Whittaker 的若干猜想。这些工作推动了拓扑动力系统与算子代数交叉领域的发展，已成为后续研究的重要基础。

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