10:00 to 11:00 George Elliott (University of Toronto); (Cardiff University); (University of Copenhagen)The classification of unital simple separable C*-algebras with finite nuclear dimension As, perhaps, a climax to forty years of work by many people, the class of algebras in the title (assumed also to satisfy the UCT, which holds in all concrete examples and may be automatic) can now be classified by means of elementary invariants (the K-groups and tracial simplex). INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Stuart White (University of Glasgow)The structure of simple nuclear C*-algebras: a von Neumann prospective I'll discuss aspects of structure of simple nuclear C*-algebras ( in particular the Toms-Winter regularity conjecture) drawing parallels with results for injective von Neumann algebras. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:30 Wilhelm Winter (Universität Münster)Structure and classification of nuclear C*-algebras: The role of the UCT The question whether all separable nuclear C*-algebras satisfy the Universal Coefficient Theorem remains one of the most important open problems in the structure and classification theory of such algebras. It also plays an integral part in the connection between amenability and quasidiagonality. I will discuss several ways of looking at the UCT problem, and phrase a number of intermediate questions. This involves the existence of Cartan MASAS on the one hand, and certain kinds of embedding problems for strongly self-absorbing C*-algebras on the other. INI 1 14:30 to 15:30 Sam Evington (University of Glasgow)W$^*$-Bundles and Continuous Families of Subfactors W$^*$-bundles were first introduced by Ozawa, motivated by work on the Toms-Winter Conjecture and, more generally, the classification of C$^*$-algebras.I will begin with a brief introduction to W$^*$-bundles, explaining how they combine the measure theoretic nature of tracial von Neumann algebras with the topological nature of C$^*$-algebras. I will then discuss the relationship between the triviality problem for W$^*$-bundles and the Toms-Winter Conjecture. Finally, I will present my work with Ulrich Pennig on locally trivial W$^*$-bundles and my ongoing work on expected subbundles of W$^*$-bundles inspired by subfactor theory. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Koichi Shimada (Kyoto University)A classification of real-line group actions with faithful Connes--Takesaki modules on hyperfinite factors   We classify certain real-line-group actions on (type III) hyperfinite factoers, up to cocycle conjugacy. More precisely, we show that an invariant called the Connes--Takesaki module completely distinguishs actions which are not approximately inner at any non-trivial point. Our classification result is related to the uniqueness of the hyperfinite type III_1 factor, shown by Haagerup, which is equivalent to the uniquness of real-line-group actions with a certain condition on the hyperfinite type II_{\infty} factor. We classify actions on hyperfinite type III factors with an analogous condition. The proof is based on Masuda--Tomatsu's recent work on real-line-group actions and the uniqueness of the hyperfinite type III_1 factor. INI 1
 10:00 to 11:00 Stefaan Vaes (KU Leuven)Classification of free Araki-Woods factors Co-authors: Cyril Houdayer (Université Paris Sud) and Dimitri Shlyakhtenko (UCLA).Free Araki-Woods factors are a free probability analog of the type III hyperfinite factors. They were introduced by Shlyakhtenko in 1996, who completely classified the free Araki-Woods factors associated with almost periodic orthogonal representations of the real numbers. I present a joint work with Houdayer and Shlyakhtenko in which we completely classify a large class of non almost periodic free Araki-Woods factors. The key technical result is a deformation/rigidity criterion for the unitary conjugacy of two faithful normal states on a von Neumann algebra. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Dima Shlyakhtenko (University of California, Los Angeles)Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions Co-authors: Sorin Popa (UCLA) and Stefaan Vaes (Leuven)We introduce L$^2$-Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasi-regular symmetric enveloping inclusion of II$_1$ factors. We actually develop a (co)homology theory for arbitrary quasi-regular inclusions of von Neumann algebras. For crossed products by countable groups Γ, we recover the ordinary (co)homology of Γ. For Cartan subalgebras, we recover Gaboriau's L$^2$-Betti numbers for the associated equivalence relation. In this common framework, we prove that the L$^2$-Betti numbers vanish for amenable inclusions and we give cohomological characterizations of property (T), the Haagerup property and amenability. We compute the L$^2$-Betti numbers for the standard invariants of the Temperley-Lieb-Jones subfactors and of the Fuss-Catalan subfactors, as well as for free products and tensor products. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:30 Arnaud Brothier (Università degli Studi di Roma Tor Vergata)Crossed-products by locally compact groups and intermediate subfactors. I will present examples of an action of a totally disconnected group G on a factor Q such that intermediate subfactors between Q and the crossed-product correspond to closed subgroups of G. This extends previous work of Choda and Izumi-Longo-Popa. I will discuss about the analytical difference with the case of actions of discrete groups regarding the existence of conditional expectations or operator valued weights. Finally I will talk about intermediate subfactors in the context of actions of Hecke pairs of groups. This is a joint work with Rémi Boutonnet. INI 1 14:30 to 15:30 Alexei Semikhatov (Lebedev Physical Institute)Screening operators in conformal field models and beyond INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Alice Guionnet (ENS - Lyon)tba INI 1 19:30 to 22:00 Formal Dinner at Emmanuel College