Characterization of zero singular ideal in non-Hausdorff groupoid C*-algebras

Abstract: Non-Hausdorff etale groupoids arise naturally from interesting dynamical systems and as models of important classes of $C^*$-algebras. One of the main obstacles in understanding the associated $C^*$-algebras in terms of their groupoids is the existence of a possibly non-zero ideal consisting of functions supported on meagre sets which, for instance, obstructs characterizing simplicity in terms of the usual groupoid properties in the Hausdorff setting. In this talk, I discuss my result characterizing when this "singular" ideal is zero in terms of a groupoid property. I will discuss the methods I use in the proofs, including the use of the Hausdorff cover of a non-Hausdorff groupoid, introduced by Timmermann, and a new concept of "compressing" linear maps to *-homomorphisms. This talk is based on my preprint arxiv.org/abs/2509.07262.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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