Representations of Groupoid C*-algebras and Fredholm Groupoids

Yu Qiao ÇÇÓê

*(Shaanxi Normal University)*

15:30-16:30, June 8, 2018 Science Building A504

__Abstract:__

In the 1980s, Alain Connes initiated his program of noncommutative
differential geometry, especially the study of ¡°bad¡± spaces. It turns out that (Lie) groupoids are an effective tool to model many analysis and index problems on singular
spaces. In this talk, we first review the construction of group C*-algebras via the
representation theory of groups, the notion of Lie groupoids, and the construction of
groupoid C
∗
-algebras via the representation theory of C
∗
-algebras. Then we give the
concept of a Fredholm groupoid, in some sense, the largest class of groupoids for which
certain Fredholm criteria hold with respect to a natural class of representations, namely
the regular representations of a groupoid. Finally we investigate the relations among Fredholm groupids and some families of representations of groupoid C*-algebras. This is joint work with Catarina Carvalho and Victor Nistor.

__About the speaker:__

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