Speaker: Valerio Proietti (University of Oslo)
Time: 2025-11-07 16:30-15:30
Location: 1410, SIMIS
Abstract: For an ample groupoid with torsion-free stabilizers, I will sketch the construction of a Chern character map going from the domain of the Baum–Connes assembly map of G to the groupoid homology groups of G with rational coefficients. As a main application, assuming the (rational) Baum–Connes conjecture, we prove the rational form of Matui’s HK conjecture, i.e., we show that the operator K-groups of the groupoid C*-algebra are rationally isomorphic to the periodicized groupoid homology groups. The construction hinges on element of homotopy theory. I will discuss applications to the Elliott invariant of classifiable C*-algebras.
About Speaker: Valerio Proietti is a young scholar whose research spans K-theory, groupoid homology, dynamical systems, index theory, and quantum groups. He has made significant contributions to the Baum–Connes conjecture and homology theory for groupoids. His achievements include establishing a new model for groupoid homology with Yamashita, revealing a profound connection between Matui’s HK-conjecture and the Baum–Connes conjecture for groupoids, and resolving several conjectures posed by Putnam and by Putnam–Kaminker–Whittaker.
简体中文 
English