Workshop on the Thompson Groups ## Odense, August 15-17, 2016## Visitors:- Valerio Proietti (KU), 28 May, 2017
- Magnus Goffeng (Gothenburg), 4 May, 2017
- James J. Walton (University of Leicester), 23 - 26 January, 2017
- Valerio Proietti (University of Copenhagen), 24 January, 2017
- Gabor Szabo (Münster University), 26 January, 2017
- Piotr Hajac (Warsaw), 7 February, 2017
- Ryszard Nest (KU), 9 February, 2017
- Philip Dowerk (KU Leuven), 2 March, 2017
- Ulrich Pennig (University of Muenster), Germany, 3-4 December, 2015
- Tomasz Brzeziński, Swansea University, UK, 6-10 December, 2015
- Andreas Næs Aaserud, UCLA, USA, 17 December, 2015
- Kristian Knudsen Olesen, University of Copenhagen, DK, 7 January, 2016
- Thomas Schick (University of Göttingen), 21 April, 2016
- Sean Cleary (The city college of New York), USA, 26 April, 2016
- Juhani Koivisto (Helsinki), USA, 28 April, 2016
- Dennis Hendrikx (Radboud University Nijmegen), 10 May, 2016
- Bram Mesland (Hannover), 12 May, 2016
## Talks:- Previous talks
- Thursday, May 18, 2017 2:15 - 3:15 pm. Valerio Proietti (KU), Title:C*-algebras from Axiom A spheres
ABSTRACT: Axiom A systems are a classical topic of interest in differentiable dynamics. These systems admit a "spectral" decomposition in irreducible pieces for which it is possible to define an associated C*-algebra. In the talk I'll explain how to assemble this data to define a C*-algebra that encodes the global dynamical behavior of the system. Two and three dimensional spheres will provide some examples. - Thursday, May 4, 2017 2:15 - 3:15 pm. Magnus Goffeng (Gothenburg), Title: Boundaries and/of noncommutative geometry
ABSTRACT: While spectral triples are the analogue of complete manifolds in noncommutative geometry, it remains unclear if there is a noncommutative description of manifolds with boundaries. We discuss one approach to introducing boundaries into spectral triples: relative spectral triples. This approach come with good KK-theoretical properties, but computing what the boundary is provides a technical challenge. Based on joint work with Iain Forsyth, Bram Mesland, and Adam Rennie. - Thursday, April 20, 2017 2:15 - 3:15 pm. Wojciech Szymanski (SDU), Title: On permutation representations of the Thompson group F
ABSTRACT: I will define an interesting family of transitive, permutation representations of the Thompson group F, and discuss in some detail one of them. I will then show that this representation admits an F-equivariant compactification, with the underlying space consisting of infinite trees. - Thursday, April 6, 2017 2:15 - 3:15 pm. Tron Omland (Oslo), Title: C*-simplicity and radical classes of groups
ABSTRACT: We define radical and residual classes of groups, and explain that there exists a radical detecting C*-simplicity, in a similar way as the amenable radical detects the unique trace property. The talk is based on joint work with Nikolay A. Ivanov from Sofia University, Bulgaria. - Thursday, March 30, 2017 2:15 - 3:15 pm. Stuart White (Glasgow), Title: C*-rigid groups
ABSTRACT: In the context of group operator algebras, rigidity results allow the underlying group to be determined from knowledge of the operator algebra. Remarkable progress was made in 2012 by Ioana, Popa and Vaes when they identified the first examples of von Neumann rigid groups. This talk, based on joint work with Knudby, Raum and Thiel, will discuss what's known in the setting of C*-algebras.rresponding partial crossed product C*-algebras will be Morita equivalent to tame separated graph C*-algebras. This is joint work with Pere Ara. - Thursday, March 23, 2017 2:15 - 4:00 pm.
Title: Graf theory afternoon
Brooks' Theorem and Beyond Michael Stiebitz, Technische Universit\"at Ilmenau. Joint work with Bjarne Toft, IMADA Brooks' theorem from 1941 relates the chromatic number $\chi$ to the maximum degree $\De$ of a graph. So $\cn(G)\leq \De(G)+1$ and equality holds if and only if $G$ has a component which is a complete graph or an odd cycle. In a recent paper Alboulker, Brettell, Havet, Marx, and Trotignon investigated relations between the chromatic number and connectivity parameters of graphs. So let $\la(G)$ denote the maximum local edge connectivity of a graph $G$. As already observed by Dirac in the 1950s every graph satisfies $\cn(G)\leq \la(G)+1$. In the talk we will present a complete description of the class of graphs $G$ satisfying $\cn(G)=\la(G)+1$. This leads to a polynomial algorithm that for any fixed $k$, and for any given $G$ with $\la(G)\leq k+1$, either finds a coloring of $G$ with $k$ colors or a certificate proving that such a coloring cannot exists. This provides a positive answer to a conjectured made by Alboulker, Brettell, Havet, Marx, and Trotignon. Degree choosable signed graphs Thomas Schweser, Technische Universit\"at Ilmenau, Germany A signed graph is a graph in which each edge is labeled with $+1$ or $-1$. A (proper) vertex coloring of a signed graph $G$ is a mapping $\phi$ that assigns to each vertex $v\in V(G)$ a color $\phi(v)\in \mathbb{Z}$ such that every edge $vw$ of $G$ satisfies $\phi(v)\not= \sigma(vw)\phi(w)$, where $\sigma(vw)$ is the sign of the edge $vw$. For an integer $h\geq 0$, let $Z_{2h}=\{\pm1,\pm2, \ldots, \pm h\}$ and $Z_{2h+1}=Z_{2h} \cup \{0\}$. The chromatic number $\chi(G)$ of the signed graph $G$ is the least integer $k$ such that $G$ admits a vertex coloring $\phi$ with $\textrm{im}(\phi)\subseteq Z_k$. As proved by M\'a\v{c}ajov\'a, Raspaud and \v{S}koviera, every signed graph $G$ satisfies $\chi(G)\leq \Delta(G)+1$ and there are three types of signed connected simple graphs for which equality holds. We will present a list version of this result by characterizing degree choosable signed (multi-)graphs. - Thursday, March 16, 2017 2:15 - 3:15 pm. Matias Lolk (KU), Title: Separated graphs and convex subshifts
ABSTRACT: It is easily seen that any subshift (over a finite alphabet) of finite type may be represented as the edge shift of a finite directed graph. Moreover, when viewing any such one-sided subshift as a partial action of the free group on the alphabet, the associated partial crossed product C*-algebra is exactly the corresponding graph C*-algebra. In this talk, we will introduce a wider class of partial dynamical systems called "convex subshifts": the fundamental idea is to give up the linear structure of a sequence and consider data stored in trees instead. We will then define the notion of a finite type convex subshift and indicate why it may represented, up to Kakutani equivalence, as the partial action associated with a so-called separated graph. In particular, the corresponding partial crossed product C*-algebras will be Morita equivalent to tame separated graph C*-algebras. This is joint work with Pere Ara. - Thursday, March 2, 2017 2:15 - 3:15 pm. Philip Dowerk (Leuven), Title: Bounded normal generation
ABSTRACT: In this talk I will present joint work with Andreas Thom on bounded normal generation (BNG) for projective unitary groups of von Neumann algebras. We say that a group has (BNG) if the conjugacy class of every nontrivial element and of its inverse generate the whole group in finitely many steps. I will explain the strategy to prove (BNG) for the projective unitary group of a finite factor. Moreover, I plan to present applications to automatic continuity of homomorphisms to separable SIN groups and the uniqueness of the Polish group topology. - Tirs, January 24, 2017 2:15 - 4:15 pm. James Walton (University of York), Title: Visualising and computing invariants of patterns via pattern-equivariant Poincaré duality
ABSTRACT: A decoration of Euclidean space is aperiodically ordered if it lacks translational symmetry and yet is still, in a some sense, highly ordered. The most famous examples of aperiodic order are the Penrose tilings which, despite lacking translational symmetries, have the property that any given finite patch may be found within some fixed radius (depending only on that patch) of any point of the tiling. In this talk I shall explain how one begins to study these systems topologically, by associating to them moduli spaces of associated families of patterns. These techniques are closely related to approaches via noncommutative geometry, which establish a connection to physical properties of quasicrystals based upon these patterns. Topological invariants of these 'pattern spaces' may often by interpreted in a highly geometric way via the so-called pattern-equivariant (PE) formalism, first introduced by Kellendonk and Putnam. I shall explain how these invariants can be given approachable alternative depictions via a Poincaré duality result, using the Penrose tilings as our running example. The resulting PE homology groups can be directly computed for tilings with a hierarchical structure. The PE homology may be incorporated into a calculation of the Čech cohomology of the Euclidean hull of the Penrose tilings. - Tirs, January 26, 2017 2:15 - 3:15 pm. Gabor Szabo (Münster University), Title: Ocneanu-type uniqueness for certain group actions on strongly self-absorbing C*-algebras
ABSTRACT: The classification problem for amenable group actions on injective factors emerged as a natural aim after Connes’ phenomenal classification results in the 70s, which involved the classification of cyclic group actions on type II-factors. After Jones’ breakthrough for finite group actions, it was Ocneanu who settled the type II case for all amenable groups in the 80s, in particular verifying that every amenable group has a unique cocycle conjugacy class for outer actions on the hyperfinite II_1-factor. Viewing strongly self-absorbing C*-algebras as the natural C*-algebraic analogs of the hyperfinite II_1-factor, it is natural to ask whether Ocneanu’s result can hold its ground in this setting. That is, for a given amenable group G and a strongly self-absorbing C*-algebra D, is there a unique cocycle conjugacy class for strongly outer G-actions on D? It is by now well-known that such rigid behavior is obstructed by torsion in G, but I will argue why the answer to the aforementioned question could be ‘Yes’ for torsion-free groups. As of yet, however, this problem remained open even for Z3-actions on the Jiang-Su algebra. I will explain how the theory of strongly self-absorbing actions can be employed to settle this problem in the abelian case, and maybe even far beyond that..
## Uffe Haagerup
## Members: |

## Contact information:
## Research interests:My research mainly concerns the theory of C*-algebras, with particular focus on topological K-theory for C*-algebras, the theory of C*-dynamical systems and of crossed product C*-algebras by groups or groupoids, also with regards to applications to the Elliott classification program of separable, nuclear C*-algebras. I am moreover interested in algebraic topology and its connections to operator algebras. |

(Postdoc)

## Contact information:
## Research interests:My research interests include geometric group theory and large scale geometry. In the past, I have worked on fixed point properties of uniformly bounded group actions on Hilbert spaces using techniques from L^2-cohomology; non-amenability of hyperbolic cones with applications to visual Gromov hyperbolic spaces; and characterising non-amenability, or more generally the vanishing of the fundamental class in controlled coarse homology, of metric measure spaces with applications to locally compact compactly generated groups. |

(Associate professor)

## Contact information:
## Research interests:My research revolves around the interplay between operator algebras, group theory and geometry, with emphasis on topics such as quantum groups, von Neumann algebras, $L^2$-Betti numbers and cohomology. Most recently, my research has been focused on various aspects of the theory of topological groups, including cohomological invariants of nilpotent Lie groups and automatic continuity properties of certain automorphism groups. |

(Postdoc)

## Contact information:
## Research interests:My research interests are Non commutative geometry, C*-algebras, Von Neumann algebras, Geometric Group Theory (in particular the Thompson groups F, T, V), theory of tilings, dynamical systems, differential geometry, circle packings, geometric transversal theory. |

(Professor)

## Contact information:
## Research interests:C*-algebras and their symmetries provided by endomorphisms, automorphisms and (discrete) group actions. Cuntz algebras, their endomorphisms, automorphisms, and discrete subgroups of their unitary groups. Graph algebras, their endomorphisms and automorphisms, especially via a combinatorial and computer supported experimental approach. Applications of graph algebras to noncommutative geometry. Fell bundles, systems of Hilbert bimodules, and their C*-algebras, from both analytic and algebraic points of view. |

(Ph.D. student)

## Contact information:
## Research interests:Advisor: David Kyed.TBA. |

(Assistant professor)

## Contact information:
## Research interests:My main research interest is noncommutative geometry. More specifically I am working on the development of an unbounded version of KK-theory where the Kasparov product has an explicit description. I also have a keen interest in secondary invariants of algebraic K-theory and in index-type theorems for elliptic differential operators on non-compact manifolds. |

Address: Institut for Matematik og Datalogi Syddansk Universitet Campusvej 55 DK-5230 Odense M. |
Contact: Maria Ramirez-Solano solano@imada.sdu.dk |