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Priority Research Centre for Computer-Assisted
Research Mathematics and its Applications

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CARMA-Sponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]

  • Location: Room Purdue Room, Great Hall (Callaghan Campus) The University of Newcastle
  • Dates: Fri, 15th Mar 2019 - Fri, 15th Mar 2019
  • Schedule:

    12-1: Mathai Varghese
    1-2: Lunch
    2-3: Fedor Sukochev
    3-3.30: Tea
    3.30-4.30: George Willis
    Evening: Dinner

  • Speaker: ARC Laureate Fellow George Willis, CARMA, The University of Newcastle
  • Title: Zero-Dimensional Symmetry and its Ramifications
  • Abstract for Zero-Dimensional Symmetry and its Ramifications:
         This project aims to investigate algebraic objects known as 0-dimensional groups, which are a mathematical tool for analysing the symmetry of infinite networks. Group theory has been used to classify possible types of symmetry in various contexts for nearly two centuries now, and 0-dimensional groups are the current frontier of knowledge. The expected outcome of the project is that the understanding of the abstract groups will be substantially advanced, and that this understanding will shed light on structures possessing 0-dimensional symmetry. In addition to being cultural achievements in their own right, advances in group theory such as this also often have significant translational benefits. This will provide benefits such as the creation of tools relevant to information science and researchers trained in the use of these tools.

  • Speaker: ARC Laureate Fellow Mathai Varghese, The University of Adelaide
  • Title: Advances in Index Theory
  • Abstract for Advances in Index Theory:
         The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant's expertise in the area, the project will involve postgraduate and postdoctoral training in order to enhance Australia's position at the forefront of international research in Geometric Analysis. Ultimately, the project will enhance Australia's leading position in the area of Index Theory by developing novel techniques to solve challenging conjectures, and mentoring HDR students and ECRs.

  • Speaker: ARC Laureate Fellow Fedor Sukochev, University of NSW
  • Title: Breakthrough methods for noncommutative calculus
  • Abstract for Breakthrough methods for noncommutative calculus:
         This project aims to solve hard, outstanding problems which have impeded our ability to progress in the area of quantum or noncommutative calculus. Calculus has provided an invaluable tool to science, enabling scientific and technological revolutions throughout the past two centuries. The project will initiate a program of collaboration among top mathematical researchers from around the world and bring together two separate mathematical areas into a powerful new set of tools. The outcomes from the project will impact research at the forefront of mathematical physics and other sciences and enhance Australia's reputation and standing.
  • [Permanent event link]

  • Location: Room W104, Behavioural Sciences Building (Callaghan Campus) The University of Newcastle
  • Dates: Fri, 1st Mar 2019 - Fri, 1st Mar 2019
  • Schedule:

    12-1: Marcelo Laca
    1-2: Lunch
    2-3: Zahra Afsar
    3-3.30: Tea
    3.30-4.30: Aidan Sims
    Evening: Dinner

  • Speaker: Dr Zahra Afsar, The University of Sydney
  • Title: KMS states of $C^*$-algebras of $*$-commuting local homeomorphisms and applications in $k$-graph algebras.
  • Abstract for KMS states of $C^*$-algebras of $*$-commuting local homeomorphisms and applications in $k$-graph algebras.:
         In this talk, I will show how to build $C^*$-algebras using a family of local homeomorphisms. Then we will compute the KMS states of the resulted algebras using Laca-Neshveyev machinery. Then I will apply this result to $C^*$-algebras of $K$-graphs and obtain interesting $C^*$-algebraic information about $k$-graph algebras. This talk is based on a joint work with Astrid an Huef and Iain Raeburn.

  • Speaker: Prof. Marcelo Laca, University of Victoria
  • Title: An introduction to KMS states and two suprising examples
  • Abstract for An introduction to KMS states and two suprising examples:
         The KMS condition for equilibrium states of C*-dynamical systems has been around since the 1960’s. With the introduction of systems arising from number theory and from semigroup dynamics following pioneering work of Bost and Connes, their study has accelerated significantly in the last 25 years. I will give a brief introduction to C*-dynamical systems and their KMS states and discuss two constructions that exhibit fascinating connections with key open questions in mathematics such as Hilbert’s 12th problem on explicit class field theory and Furstenberg’s x2 x3 conjecture.

  • Speaker: Prof. Aidan Sims, University of Wollongong
  • Title: What equilibrium states KMS states for self-similar actions have to do with fixed-point theory
  • Abstract for What equilibrium states KMS states for self-similar actions have to do with fixed-point theory:
         Using a variant of the Laca-Raeburn program for calculating KMS states, Laca, Raeburn, Ramagge and Whittaker showed that, at any inverse temperature above a critical value, the KMS states arising from self-similar actions of groups (or groupoids) $G$ are parameterised by traces on C*(G). The parameterisation takes the form of a self-mapping \chi of the trace space of C*(G) that is built from the structure of the stabilisers of the self-similar action. I will outline how this works, and then sketch how to see that \chi has a unique fixed-point, which picks out the ``preferred" trace of C*(G) corresponding to the only KMS state that persists at the critical inverse temperature. The first part of this will be an exposition of results of Laca-Raeburn-Ramagge-Whittaker. The second part is joint work with Joan Claramunt.
  • [Permanent event link]

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