Vikki Quigley (University of Sheffield)
Graded K-theory and analytic assembly
Much of the early development of operator K-theory uses C*-algebras which are equipped with a grading. In this case, it is possible to present a theory which works equally well for complex and real C*-algebras. In this talk I will introduce the idea of graded K-theory, and explain how important properties, such as Bott periodicity, are very simple to prove in this setting. In the second part of the talk I will give a possible application of this theory to the study of manifolds of positive scalar curvature.
El-Kaioum Mohamed Moutuou (University of Southampton)
Fell bundles over 2-groupoids
Fell bundles over groupoids were introduced by Kumjian; they can be thought of as groupoid actions by Hilbert bimodules on C*-algebras. In fact, C*-algebras and Hilbert bimodules form a nice weak (2,1)-category that allows a natural generalisation of Fell bundles for 2-groupoids. In this talk I will outline a few basics of 2-category theory with special emphasis on the 2-category of C*-algebras, and introduce in a functorial way Fell bundles for 2-groupoids. (This is ongoing joint work with Ralf Meyer)
Otogo Uuye (University of Cardiff)
The Fubini product of operator spaces
The interplay between geometric group theory and functional analysis is an immensely rich subject. In this talk, we give a gentle introduction a particularly useful functional analytical device called the Fubini product and look at its application to the approximation property of groups.