• Matthew Daws, Lancaster University

Functional Analytic modules 

I will talk about some aspects of Banach Algebra theory.  I imagine my audience will mostly be students of Operator Algebras, or from further-afield areas of Functional Analysis.  As such, I will look at a range of examples, showing how things are similar, or differ, from purely algebraic settings, or from Operator Algebras.  I will focus on module theory, and perhaps think about Hilbert C*-modules, and what a Banach Algebra analogue might be.  This will be a survey talk, rather than looking at any particularly new results.

• Jonathan Hickman, University of Edinburgh

On convergence of Fourier integrals

In the first half of the 20th century great advances were made in understanding convergence of Fourier series and integrals in one dimension. Many natural convergence problems in higher dimensions are still poorly understood, however, despite great attention by many prominent mathematicians over the last five decades. In this gentle talk I will introduce the basic questions, describe their rich underlying geometry, and explain some recent developments in various joint works which have applied tools from incidence and algebraic geometry to these problems. 

• Ying-Fen Lin, Queen’s University Belfast

Twisted groupoid algebras 

While groupoid C*-algebras play a fundamental role in theory and include many important classes, their purely algebraic analogues, Steinberg algebras, have proven themselves to be useful and provide interesting insights. In this talk, I will demonstrate how (twisted) groupoids and their associated algebras serve as a useful tool to bridge the gap between abstract algebra and analysis. If time permits, I will introduce different but more general subalgebras than Cartan’s in abstract algebra and analysis sittings which also give rise Kumjian-Renault theory.

• Mike Whittaker, University of Glasgow

Katsura-Exel-Pardo algebras 

Takeshi Katsura proved that every Kirchberg algebra arises, up to strong Morita equivalence, from a C*-algebra associated to two integer matrices. Exel and Pardo realised that Katsura's construction gives rise to a self-similar group(oid) action on the path space of a graph, and that Katsura's C*-algebra is the associated Cuntz-Pimsner algebra of the self-similar action. I'll introduce these algebras and some recent research into their properties as noncommutative dynamical systems. 

• Safoura Zadeh, University of Bristol

Dilation technique in operator algebra 

Dilation theory provides a framework for understanding operators by realizing them as compressions of larger, better-behaved operators. Classical results, such as those of Sz.-Nagy, Stinespring, Akcoglu, and Rota, illustrate how this approach leads to deeper structural insights. In this talk, I will introduce some of the fundamental dilation results and discuss some applications. I will also highlight an obstruction to extending Akcoglu’s dilation theorem to the noncommutative setting.