Queen's University Belfast

Groupoid C*-algebras and twisted groupoid C*-algebras are introduced by Renault in the late ’70. Twisted groupoid C*-algebras have since proved extremely important in the study of structural properties for large classes of C*-algebras. On the other hand, Steinberg algebras are introduced independently by Steinberg and Clark, Farthing, Sims and Tomforde around 2010 which are a purely algebraic analogue of groupoid C*-algebras. Steinberg algebras provide useful insight into the analytic theory of groupoid C*-algebras and give rise to interesting examples of *-algebras. In this talk, I will first recall some relevant background on topological groupoids and twisted groupoid C*-algebras, then I will introduce twisted Steinberg algebras which generalise the Steinberg algebras and provide a purely algebraic analogue of twisted groupoid C*-algebras. If I have enough time, I will further introduce pair of algebras which consist of a Steinberg algebra and an algebra of locally constant functions on the unit space, it is an algebraic analogue of Cartan pairs

The study of non-local games has involved fruitful interactions between operator algebra theory and quantum physics, with a starting point the link between the Connes Embedding Problem and the Tsirelson Problem, uncovered by Junge et al (2011) and Ozawa (2013). Particular instances of non-local games, such as binary constraint system games and synchronous games, have played an important role in the pursuit of the resolution of these problems. In this talk, I will summarise part of the operator algebraic toolkit that has proved useful in the study of non-local games and of their perfect strategies, highlighting the role C*-algebras and operator systems play in their mathematical understanding.

Persistent homology is an algebraic tool for quantifying topological features of shapes and functions, which has recently found wide applications in data and shape analysis. In the first and introductory part of this talk I recall the underlying ideas and basic concepts of this very active field of research. In the second part, I plan to sketch a concrete application of this concept to digital image processing. 

TBA