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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 W 238, Behavioural Sciences (Callaghan Campus) The University of Newcastle
  • Dates: Fri, 3rd May 2019 - Sun, 3rd Mar 2019
  • Schedule:

    12-1: Heiko Dietrich
    1-2: Lunch
    2-3: Youming Qiao
    3-3.30: Tea
    3.30-4.30: Nicole Sutherland

  • Speaker: Dr Heiko Dietrich, Monash University
  • Title: Quotient algorithms (a.k.a. how to compute with finitely presented groups)
  • Abstract for Quotient algorithms (a.k.a. how to compute with finitely presented groups):
         In this talk, I will survey some of the famous quotient algorithms that can be used to compute efficiently with finitely presented groups. The last part of the talk will be about joint work with Alexander Hulpke (Colorado State University): we have looked at quotient algorithms for non-solvable groups, and I will report on the findings so far.

  • Speaker: Dr Youming Qiao, University of Technology Sydney
  • Title: Isomorphism testing problems: in light of Babai’s graph isomorphism breakthrough
  • Abstract for Isomorphism testing problems: in light of Babai’s graph isomorphism breakthrough:
         In computer science, an isomorphism testing problem asks whether two objects are in the same orbit under a group action. The most famous problem of this type has been the graph isomorphism problem. In late 2015, L. Babai announced a quasipolynomial-time algorithm for the graph isomorphism problem, which is widely regarded as a breakthrough in theoretical computer science. This leads to a natural question, that is, which isomorphism testing problems should naturally draw our attention for further exploration?

  • Speaker: Dr Nicole Sutherland, The University of Sydney
  • Title: Computations of Galois groups and splitting fields
  • Abstract for Computations of Galois groups and splitting fields:
         The Galois group of a polynomial is the automorphism group of its splitting field. These automorphisms act by permuting the roots of the polynomial so that a Galois group will be a subgroup of a symmetric group. Using the Galois group the splitting field of a polynomial can be computed more efficiently than otherwise, using the knowledge of the symmetries of the roots. I will present an algorithm developed by Fieker and Klueners, which I have extended, for computing Galois groups of polynomials over arithmetic fields as well as approaches to computing splitting fields using the symmetries of the roots.
  • [Permanent event link]

  • Location: Room W 238, Behavioural Sciences (Callaghan Campus) The University of Newcastle
  • Dates: Fri, 5th Apr 2019 - Fri, 5th Apr 2019
  • Schedule:

    12-1: Talk 1
    1-2: Lunch
    2-3: Talk 2
    3-3.30: Tea
    3.30-4.30: Talk 3

  • Speaker: Dr Arnaud Brothier, University of NSW
  • Title: Jones' actions of the Thompson's groups: applications to group theory and mathematical physics
  • Abstract for Jones' actions of the Thompson's groups: applications to group theory and mathematical physics:
         Motivating in constructing conformal field theories Jones recently discovered a very general process that produces actions of the Thompson groups $F$,$T$ and $V$ such as unitary representations or actions on $C^{\ast}$-algebras. I will give a general panorama of this construction along with many examples and present various applications regarding analytical properties of groups and, if time permits, in lattice theory (e.g. quantum field theory).

  • Speaker: Dr Lawrence Reeves, The University of Melbourne
  • Title: An irrational-slope Thompson's group
  • Abstract for An irrational-slope Thompson's group:
         Let $t$ be the the multiplicative inverse of the golden mean. In 1995 Sean Cleary introduced the irrational-slope Thompson's group $F_t$, which is the group of piecewise-linear maps of the interval $[0,1]$ with breaks in $Z[t]$ and slopes powers of $t$. In this talk we describe this group using tree-pair diagrams, and then demonstrate a finite presentation, a normal form, and prove that its commutator subgroup is simple. This group is the first example of a group of piecewise-linear maps of the interval whose abelianisation has torsion, and it is an open problem whether this group is a subgroup of Thompson's group $F$.

  • Speaker: Dr Richard Garner, Macquarie University
  • Title: Topos-theoretic aspects of self-similarity
  • Abstract for Topos-theoretic aspects of self-similarity:
         A Jonsson-Tarski algebra is a set X endowed with an isomorphism $X\to XxX$. As observed by Freyd, the category of Jonsson-Tarski algebras is a Grothendieck topos - a highly structured mathematical object which is at once a generalised topological space, and a generalised universe of sets.
    In particular, one can do algebra, topology and functional analysis inside the Jonsson-Tarski topos, and on doing so, the following objects simply pop out: Cantor space; Thompson's group V; the Leavitt algebra L2; the Cuntz semigroup S2; and the reduced $C^{\ast}-algebra of S2. The first objective of this talk is to explain how this happens.
    The second objective is to describe other "self-similar toposes" associated to, for example, self-similar group actions, directed graphs and higher-rank graphs; and again, each such topos contains within it a familiar menagerie of algebraic-analytic objects. If time permits, I will also explain a further intriguing example which gives rise to Thompson's group F and, I suspect, the Farey AF algebra.
    No expertise in topos theory is required; such background as is necessary will be developed in the talk.
  • [Permanent event link]

  • 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

  • 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

  • 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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