Andrew Hawkins: A twisted spectral triple on the Cuntz algebra
The non-existence of a finite trace on the Cuntz algebra prevents the possibility of constructing spectral triples with good summability properties. On the other hand, Connes and Moscovici present an abstract definition of a twisted spectral triple for which the resultant Dixmier functional satisfies a natural KMS condition. When the Cuntz algebra is viewed as an Exel crossed product of a subshift space by an endomorphism, the twisting can be interpreted as a scaling factor associated to the shift action. We suggest one possible way of writing down a twisted spectral triple for a large class of Cuntz-Krieger algebras using these ideas.
David O'Sullivan: C*-categories
A C*-category is a categorification of a C*-algebra in the same sense that a groupoid is a generalisation of a group. C*-categories occur naturally when analytic assembly maps are studied - in particular one can associate to a discrete groupoid a C*-category that is in some sense more natural than the groupoid C*-algebras of Renault. In this introductory talk I will outline some of the basic theory of C*-categories, and show how a number of C*-algebraic results generalise to the level of categories. I will also outline the construction of the so-called groupoid C*-categories.
Nadia Gheith: The Coarse Cofibration Category
Baues introduced a notion of cofibration category as a generalisation of a Quillen model category. He defined it to be a category together with two classes of morphisms called cofibrations and weak equivalences such that specific axioms are satisfied. In this talk I will introduce a notion of closeness equivalence classes of coarse maps- these are maps between spaces preserving the large scale structure. And prove that the category of spaces and closeness equivalence classes with two classes of morphisms called coarse cofibration classes and coarse homotopy equivalence classes satisfy the cofibration category axioms. This category will be called the coarse cofibration category.