Lectures WS 2025/2026

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the first lecture I will discuss what an \’etale groupoid is, with particular emphasis on ample groupoids, describe some key classes of examples arising from directed graphs and their analogues, and define their homology (for this I will stick strictly to the ample case to avoid getting bogged down in technicalities) and cohomology.

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the second lecture I will introduce the *-algebras and C*-algebras of a groupoid, and outline how cohomology can be used to twist such C*-algebras, including an overview of their structure theory, and how homology relates to some of the classical algebraic invariants of a groupoid C*-algebra.

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the third lecture I will describe techniques for computing the homology of a groupoid and indicate how these computations can be used to recover some well-known computations of K-theory. I will also discuss the idea of an equivalence of ample groupoids, and discuss the relationship between groupoid equivalence and groupoid homology.