Group Actions Seminar: Tornier, Vas

The next Group Actions Seminar will be on Tuesday 28 February at the University of
Sydney.  The schedule, titles and abstracts are below.  

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12 noon-1pm, Carslaw 375 

Speaker: Stephan Tornier, ETH Zurich and University of Newcastle 

Title: p-localization of Burger-Mozes universal groups 

Abstract: The structure theory of locally compact groups can, to a large extent, be
reduced to the study of totally disconnected such groups.  This talk concerns an attempt
to take a further reduction step via p-groups.  We recall the concept of prime
localization of totally disconnected locally compact groups first introduced by Colin
Reid in 2011: For every such group G and prime p, the p-localization of G is a virtually
pro-p group which maps continuously and injectively into G with dense image, and which
behaves nicely with respect to the scale and modular function.  The talk aims to
determine said prime localization for Burger-Mozes universal groups acting on regular
trees locally like a given permutation group.  A short discussion of these groups is
followed by the main statement relating the localization to Le Boudec groups acting on
the same tree with almost prescribed local action and ideas of proof.  

1-3pm Lunch and coffee 

3-4pm, Carslaw 375 

Speaker: Lia Vas, University of the Sciences 

Title: Algebraization of Operator Theory 

Abstract: I have been working in algebra and ring theory, in particular with rings of
operators, involutive rings, Baer *-rings and Leavitt path algebras.  These rings were
introduced in order to simplify the study of sometimes rather cumbersome operator theory
concepts.  For example, a Baer *-ring is an algebraic analogue of an AW*-algebra and a
Leavitt path algebra is an algebraic analogue of a graph C*-algebra.  Such rings of
operators can be studied without involving methods of operator theory.  Thus
algebraization of operator theory is a common thread between most of the topics of my
interest.  After some overview of the main ideas of such algebraization, I will focus on
one common aspect of some of the rings of operators - the existence of a trace as a way
to measure the size of subspaces/subalgebras.  In particular, we adapt some desirable
properties of a complex-valued trace on a C*-algebra to a larger class of algebras.