13:00 - 13:50: Chris Bruce

14:00 - 14:50: Brita Nucinkis 

     15:00 - 15:30: Coffee break

15:30 - 16:20:  Xin Li

16:30 - 17:20: Takuya Takeishi

17:30 onwards: Reception

Abstract: I will give an introduction to irreversible algebraic actions and explain how they give rise to C*-algebras and ample groupoids. The C*-algebras arising this way include ring C*-algebras, Cuntz algebras, and C*-algebras for multidimensional full shifts, and the topological full groups arising from this construction may be viewed as generalisations of Thompson's group V. This talk is based on joint work with Xin Li.

Abstract:  I will give a quick introduction to Thompson’s groups V, and some of its generalisations including the Brin-Thompson groups nV, which can be interpreted as topological full groups of ample groupoids. I will then describe a method on how to find unique normal forms for elements in nV. This is joint work with Burillo and Cleary.

Abstract: This talk is about joint work with Chris Bruce on C*-algebras and groupoids arising from algebraic actions. Our original motivation was the following question in the context of ring C*-algebras, which were introduced by Joachim Cuntz: How much information do the canonical groupoid models of ring C*-algebras remember about the original ring? For rings of algebraic integers, our main result says that these groupoid models remember everything -- i.e. they determine the ring completely. My goal is to explain this result and its generalizations for other classes of algebraic actions. I will also mention connections to topological full groups and continuous orbit equivalence.

Abstract: By the work of Bruce and Li, the topological full group (TFG) of the groupoid associated to the ring C*-algebra for the ring of integers of a number field is known to be a complete invariant for number fields, but it is now clear how basic invariants of number fields are reflected in the TFG. For the first step to understand this TFG, we show that the extension degree over the rational field coincides with the smallest degree such that the group homology of the TFG does not vanish. We show it by the calculation of the groupoid homology. For another application of this computation, we give another proof of Li-Luck's computation of the K-theory of the ring C*-algebras. We also compute the groupoid homology of Barlak--Omland--Stammeier groupoids and solve the conjecture for K-theory of their C*-algebras. This is a joint work with C. Bruce and Y. Kubota.