9:45 - 10:15: Registration and welcome
10:15 - 11:25: Tristan Bice (Institute of Mathematics of the Czech Academy of Sciences)
11:25 - 11:50: Coffee
11:50 - 13:00: Jean Renault (Université d’Orléans)
13:00 - 14:20: Lunch
14:20 - 15:30: Enrique Pardo Espino (Universidad de Cádiz)
15:30 - 16:00: Coffee
16:00 - 17:10: Ali Imad Raad (American University in Bulgaria)
9:30 - 10:40: Ralf Meyer (Universität Göttingen)
10:40 - 11:10: Coffee
11:10 - 12:20: Christian Bönicke (Newcastle University)
12:10 - 14:00: Lunch
14:00 - 15:10: Jakub Curda (University of Oxford)
15:10 - 15:40: Coffee
15:40 - 16:50: Eusebio Gardella (University of Gothenburg)
19:00: Workshop Dinner at Seoul Garden
9:30 - 10:40: Marzieh Forough (Czech Technical University in Prague)
10:40 - 11:10: Coffee
11:10 - 12:20: Alistair Miller (KU Leuven)
12:10 - 14:00: Lunch
Tristan Bice: Extending the Kumjian-Renault Theory: Cartan Semigroups and Beyond
Abstract: Thanks to seminal work of Renault (2008), building on earlier work of Kumjian (1986), we know that reduced C*-algebras of twisted effective étale groupoids are precisely those containing Cartan subalgebras. A number of papers have sought to extend this beyond the effective case but some residual assumptions have always remained. In this talk we outline how to completely remove the effective assumption and even handle non-reduced C*-algebras as well by utilising what we call Cartan semigroups. Time permitting we will also discuss similar results for Steinberg algebras, including ongoing work with Malcolm Jones and Ganna Kudryavtseva extending these from ample groupoids to ample semicategories and their resulting Boolean-Cartan restriction semigroups.
Jean Renault: Boolean inverse semigroups and groupoids
Abstract: The intimate connection between groupoids and inverse semigroups has been observed long time ago. I will show that, in the case of Boolean groupoids and Boolean inverse semigroups, this connection can be expressed as an equivalence of category which extends Stone duality. In view of applications to operator algebras, I will give two complements: a twisted version of this equivalence and the realisation of any separable measure inverse semigroup as the full inverse semigroup of a second countable Boolean groupoid.
Enrique Pardo Espino: A C*-algebraic model for textile systems.
Abstract: We define a C*-algebra encoding the dynamical information of a textile system -i.e. a two-dimensional shift space-. Our approach is to construct an inverse semigroup associated to a textile system (under mild hypotheses), and then use it to construct its Exel's groupoid C*-algebra; C*-algebras of 2-graphs raise as a particular case of the construction. Also, we present an alternative construction -at a semigroup level- for textile systems in which the above strategy does not apply. The content of this talk is the first announcement of a joint work (in progress) with Elizabeth Gillaspy (U. Montana, USA) and Ying-Fen Lin (Queen's University Belfast, UK).
Ali Imad Raad: TBA
Abstract: TBA
Ralf Meyer: Groupoid models for Cuntz-Pimsner algebras
Abstract: Many generalisations of graphs such as topological, self-similar graphs may be defined as Cuntz-Pimsner algebras where the underlying C*-correspondence comes from a groupoid correspondence. In this case, the Cuntz-Pimsner algebra is also a groupoid C*-algebra. The underlying A groupoid may be characterised by a universal property, which describes its actions on spaces. This universal property also allows us to describe groupoid actors to other groupoids. These groupoid actors induce *-homomorphisms between the resulting groupoid C*-algebras. In the case of graph C*-algebras, these groupoid actors are a dynamical analogue of Cuntz-Krieger families. These generalise the relation morphisms of de Castro, D'Andrea and Hajac.
Christian Bönicke: Amalgamated products of étale groupoids
Abstract: Free products and amalgamated products are coproducts in the context of discrete groups. As exhibited by Bass-Serre theory, they play a central role in the structure theory of discrete groups and the geometric approach to group theory. In this talk I will explain how to generalise these constructions to the setting of étale groupoids by constructing the amalgamated product of two étale groupoids over a common subgroupoid. I will then discuss approximation properties and the reduced groupoid C*-algebra of an amalgamated product of groupoids. This is based on joint work in progress with my student Max Durrant.
Jakub Curda: C*-superrigidity
Abstract: A group G is called C*-superrigid if there is no other group with an isomorphic reduced C*-algebra. In 2010, Ioana, Popa and Vaes asked whether every discrete countable torsion-free group is C*-superrigid. In this talk, I will give an overview of the known examples of C*-superrigid groups and add certain classes of virtually abelian groups to the list. Finally, I will answer the question above by presenting examples of torsion-free groups which are not C*-superrigid. The proof uses recent results from classification theory of C*-algebras. This talk is based on several projects joint with subsets of Drimbe, Hua, Knudby, Patchell, Pi, Raum, Shiner, Slutsky, Thiel and White.
Eusebio Gardella: Embedding rigidity and reconstruction for L^p-groupoid algebras
Abstract: L^p-operator algebras associated with étale groupoids, for p ≠ 2, exhibit rigidity phenomena which differ sharply from the C*-algebraic case. I will give an overview of this, starting with the case of isomorphisms and then focusing on how embeddings between reduced L^p-groupoid algebras can be detected at the level of the underlying groupoids. Under natural hypotheses on the groupoids, a unital contractive homomorphism between the associated reduced L^p-operator algebras is induced by concrete groupoid data. I will explain the role of the diagonal, the normalizers, and the conditional expectation, and indicate how this reconstruction result gives useful obstructions to the existence of embeddings. I will present two applications: one to AF-embeddability, and one to embeddings into \mathcal{O}_2^p. This is joint work with Jan Gundelach.
Marzieh Forough: Quasi-equivariant lifts of completely positive maps for groupoid actions and C*-extensions
Abstract: A well-known alternate picture of KK-theory using extensions of C*-algebras was provided by Kasparov. One of the key tools in this identification is the Choi-Effros lifting theorem. This result was extended to the group equivariant setting by Thomsen. The lack of the existence of equivariant Choi-Effros theorem made Thomsen's proofs rather complicated and technical. More recently, Forough, Gardella, and Thomsen established the existence of a lift that, although not necessarily equivariant, is quasi-equivariant. In this talk, I will explain the existence of quasi-equivariant lifts of completely positive maps for locally compact Hausdorff second countable groupoid actions. Then, I will discuss how this result can lead to the problem of describing the equivariant KK-theory for groupoid actions in terms of equivariant extensions. I will represent a rephrasing of Thomsen's approach in the case of group actions, then discuss how to extend it to the groupoid equivariant setting.
Alistair Miller: Homology and K-theory for self-similar group actions
Abstract: Self-similar groups are groups of automorphisms of infinite rooted trees obeying a simple but powerful rule. Under this rule, groups with exotic properties can be generated from very basic starting data, most famously the Grigorchuk group which was the first example of a group with intermediate growth.
Nekrashevych introduced a groupoid and a C*-algebra for a self-similar group action on a tree as models for some underlying noncommutative space for the system. Our goal is to compute the K-theory of the C*-algebra and the homology of the groupoid. Our main theorem provides long exact sequences which reduce the problems to group theory. I will demonstrate how to apply this theorem to fully compute homology and K-theory through the example of the Grigorchuk group.
This is joint work with Benjamin Steinberg.