# Operator theory seminar

Title: Scattering theory and non-commutative geometry

Speaker: Alan Carey, Australian National University

Date and time:
04 Dec 2013,
3:30pm -
4:30pm

Location: CLED131

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Abstract: I organised, in collaboration with Fritz Gesztesy from Missouri, a workshop at ESI in February 2011 on the topic of this talk. Gesztesy had been working on a question in mathematical scattering theory and this talk is about developments arising from that time at ESI. The applications to quantum mechanical scattering occur in two dimensional Euclidean space with electrons moving in the presence of a magnetic field and colliding with an obstacle. (Think about impurities in a conducting layer.) The talk is organised in three parts, the first historical, about scattering theory, the second about the connection to NCG and the third on recent developments.

Title: Equilibrium states on graph algebras

Speaker: Iain Raeburn, University of Otago

Date and time:
20 Nov 2013,
3:30pm -
4:30pm

Location: CLED131

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In operator-algebraic models of physical systems, the time evolution is

given by an action of the real line on a C*-algebra, and states are given

by positive functionals on the C*-algebra. Of particular interest are the

equilibrium states, which are characterised by a property called the KMS

condition. This condition makes sense also for systems arising in purely

mathematical situations, and experience suggests that it is often of

interest to find the equilibrium states.

A thirty-year old theorem of Enomoto, Fujii and Watatani identifies the

KMS states on the C*-algebras of finite graphs. We will discuss their

theorem, and then take a new approach to it developed in joint work with

Astrid an Huef, Marcelo Laca and Aidan Sims.

Title: Homeomorphisms between aperiodic tiling spaces

Speaker: Antoine Julien, Norwegian University of Science and Technology

Date and time:
30 Oct 2013,
3:30pm -
4:30pm

Location: CLED131

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Abstract: In this talk, I will give an introduction to aperiodic tilings. Usually, one studies a topological dynamical system associated to these tilings rather than one specific tiling (this is the analogue to studying a subshift rather that one single word in symbolic dynamics). It is a natural question to ask what happens to the underlying tilings when two tiling spaces are homeomorphic. The result I will present is the following: whenever two tiling spaces are homeomorphic, the complexity function is preserved up to some multiplicative constants and rescaling.

Title: Examples of correspondences from representation theory

Speaker: Heath Emerson, University of Victoria

Date and time:
23 Oct 2013,
3:30pm -
4:30pm

Location: CLE D131

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Abstract: We describe some examples of `correspondences' related to

basic representation theory of complex semisimple Lie groups, and

derive a classical theorem of Borel on realizing highest weight

representations by means of an index theoretic construction.