
CARMASponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]
 SYMMETRY IN NEWCASTLE
 Location: Room W 238, Behavioural Sciences (Callaghan Campus) The University of Newcastle
 Dates: Fri, 3^{rd} May 2019  Sun, 3^{rd} Mar 2019

Schedule:
121: Heiko Dietrich
12: Lunch
23: Youming Qiao
33.30: Tea
3.304.30: 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 nonsolvable 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 quasipolynomialtime 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.
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 SYMMETRY IN NEWCASTLE
 Location: Room W 238, Behavioural Sciences (Callaghan Campus) The University of Newcastle
 Dates: Fri, 5^{th} Apr 2019  Fri, 5^{th} Apr 2019

Schedule:
121: Talk 1
12: Lunch
23: Talk 2
33.30: Tea
3.304.30: 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 irrationalslope Thompson's group
 Abstract for An irrationalslope Thompson's group:
Let $t$ be the the multiplicative inverse of the golden mean. In 1995 Sean Cleary introduced the irrationalslope Thompson's group $F_t$, which is the group of piecewiselinear maps of the interval $[0,1]$ with breaks in $Z[t]$ and slopes powers of $t$. In this talk we describe this group using treepair 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 piecewiselinear 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: Topostheoretic aspects of selfsimilarity
 Abstract for Topostheoretic aspects of selfsimilarity:
A JonssonTarski algebra is a set X endowed with an
isomorphism $X\to XxX$. As observed by Freyd, the category of
JonssonTarski 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 JonssonTarski 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 "selfsimilar toposes"
associated to, for example, selfsimilar group actions, directed graphs
and higherrank graphs; and again, each such topos contains within it a
familiar menagerie of algebraicanalytic 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.
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 SYMMETRY IN NEWCASTLE
 Location: Room Purdue Room, Great Hall (Callaghan Campus) The University of Newcastle
 Dates: Fri, 15^{th} Mar 2019  Fri, 15^{th} Mar 2019

Schedule:
121: Mathai Varghese
12: Lunch
23: Fedor Sukochev
33.30: Tea
3.304.30: George Willis
 Speaker: ARC Laureate Fellow George Willis, CARMA, The University of Newcastle
 Title: ZeroDimensional Symmetry and its Ramifications
 Abstract for ZeroDimensional Symmetry and its Ramifications:
This project aims to investigate algebraic objects known as 0dimensional 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 0dimensional 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 0dimensional 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.
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 SYMMETRY IN NEWCASTLE
 Location: Room W104, Behavioural Sciences Building (Callaghan Campus) The University of Newcastle
 Dates: Fri, 1^{st} Mar 2019  Fri, 1^{st} Mar 2019

Schedule:
121: Marcelo Laca
12: Lunch
23: Zahra Afsar
33.30: Tea
3.304.30: 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 LacaNeshveyev 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 selfsimilar actions have to do with fixedpoint theory
 Abstract for What equilibrium states KMS states for selfsimilar actions have to do with fixedpoint theory:
Using a variant of the LacaRaeburn 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 selfsimilar actions of groups (or groupoids) $G$ are parameterised by traces on C*(G). The parameterisation takes the form of a selfmapping \chi of the trace space of C*(G) that is built from the structure of the stabilisers of the selfsimilar action. I will outline how this works, and then sketch how to see that \chi has a unique fixedpoint, 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 LacaRaeburnRamaggeWhittaker. The second part is joint work with Joan Claramunt.
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