2012
###### Dana Williams (Dartmouth College)

3:30pm, Friday 30 November 2012

###### Title

The Equivariant Brauer Group

###### Abstract

In algebraic topology, we learn to associate groups $H^{n}(T)$ to locally compact spaces which count the $n$-dimensional holes in T''. In this talk, I want to describe how to realize $H^{3}(T)$ as a set $\mathop{\rm Br}(T)$ of equivalence classes of certain well-behaved $C^*$-algebras. The group structure imposed on $\mathop{\rm Br}(T)$ via its identification with $H^{3}(T)$ is very natural in its $C^*$-setting. With this group structure, $\mathop{\rm Br}(T)$ is called the \emph{Brauer group} of $T$. Depending on your point of view, this result can be viewed either as a concrete realization of $H^{3}(T)$ or as a classification result for a class of $C^*$-algebras. In the last part of the talk, I want to describe an equivariant version of $\mathop{\rm Br}(T)$ developed jointly with David Crocker, Alex Kumjian and Iain Raeburn. No prior knowledge of $C^{*}$-algebras or operator algebras will be assumed.

###### Xiang Xu (Michigan State University)

3:30pm, Friday 23 November 2012

###### Title

Mathematical analysis for fractional diffusion equations: modeling, forward problems and inverse problems Abstract: Time-fractional diffusion equations are of practical interest and importance, since they well describe the power law decay for the diffusion in porous media. In this talk, recent progresses on time-fractional diffusion equations are discussed, especially on some typical inverse problems, including backward problem, inverse source problem, inverse boundary problem, inverse coefficient problem etc.

###### Andrew Francis (University of Western Sydney)

3:30pm, Friday 2 November 2012

###### Title

Bacterial genome evolution with algebra!?

###### Abstract

The genome of a bacterial organism consists of a single circular chromosome that can undergo changes at several different levels. There is the very local level of errors that are introduced through the replication process, giving rise to changes in the nucleotide sequence (A,C,G,T); there are larger scale sequence changes occurring during the lifetime of the cell that are able to insert whole segments of foreign DNA, delete segments, or invert segments (among other things); and there are even topological changes that give rise to knotting in DNA. Algebra might be defined as the study of sets with structure", and has been used over the past century to describe the symmetries of nature, most especially in areas like physics and crystallography, but it also plays a role in technological problems such a cryptography. In this talk I will describe how algebraic ideas can be used to model some bacterial evolutionary processes. In particular I will give an example in which modelling the inversion process gives rise to new algebraic questions, and show how algebraic results about the affine symmetric group can be used to calculate the inversion distance" between bacterial genomes. This has applications to phylogeny reconstruction.

###### Scott Morrison (Australian National University)

3:30pm, Friday 26 October 2012

###### Title

Knots and quantum computation

###### Abstract

I'll begin with the Jones polynomial, a knot invariant discovered 30 years ago that radically changed our view of topology. From there, we'll visit the complexity of evaluating the Jones polynomial, the topological quantum field theories related to the Jones polynomial, and how all these ideas come together to offer an unorthodox model for quantum computation.

###### Peter Kim

3:30pm on 19 October 2012

###### Title

Modelling protective anti-tumour immunity using a hybrid agent-based and delay differential equation approach

###### Abstract

Although cancers seem to consistently evade current medical treatments, the body’s immune defences seem quite effective at controlling incipient tumours. Understanding how our immune systems provide such protection against early-stage tumours and how this protection could be lost will provide insight into designing next-generation immune therapies against cancer. To engage this problem, we formulate a mathematical model of the immune response against small, incipient tumours. The model considers the initial stimulation of the immune response in lymph nodes and the resulting immune attack on the tumour and is formulated as a hybrid agent-based and delay differential equation model.

###### Ngamta Thamwattana and Alexander Gerhardt-Bourke

3:30pm Friday, 5 September 2012

###### Title (Ngamta Thamwattana)

Modelling peptide nanotubes for artificial ion channels

###### Abstract

We investigate the van der Waals interaction of D,L-Ala cyclo peptide nanotubes and various ions, ion–water clusters and C60 fullerenes, using the Lennard-Jones potential and a continuum approach. Our results predict that Li+, Na+, Rb+ and Cl− ions and ion–water clusters are accepted into peptide nanotubes of 8 amino acid residues whereas the fullerene C60 molecule is rejected. The model indicates that the C60 molecule is accepted into peptide nanotubes of 12 amino acid residues, suggesting that the interaction energy depends on the size of the molecule and the internal diameter of the peptide nanotube. This result may be useful may be useful in the size-selective molecular delivery of pharmacologically active agents. Further, we also find that the ions prefer a position inside the peptide ring where the energy is minimum. In contrast, Li–water clusters prefer to be in the space between each peptide ring.

###### Title (Alexander Gerhardt-Bourke)

Continuous Logic and Operator Algebras

###### Abstract

How can we define a continuous analogy of logic, and why would we want to? We will answer both of these questions by defining continuous logic, and then seeing how we can use continuous logic to classify some special C*-algebras.

###### Sam Webster

Friday 3 August 2012

###### Title

Directed graphs and their higher dimensional analogues

###### Abstract

Last colloquium, Aidan Sims spoke about how we study C*-algebras associated to directed graphs. There is a higher-dimensional version of a directed graph called a higher-rank graph that we also like to associate C*-algebras too, but they can be a little tricky to picture and understand. I'll speak about some recent work of Aidan Sims, Iain Raeburn , Robbie Hazlewood and myself. I'll show how we can think of higher-rank graphs as directed graphs with different coloured edges and some additional hypotheses.

###### Title

Voices in bounded soft media

###### Abstract

Background information into and reasons for using polarised light beams (lasers) to formsolitons (or optical waves) in a liquid crystal will be initially discussed in this seminar. Extending from this, there will be an examination of a specific type of optical wave called an optical vortex and a brief discussion of its formation. Using this background knowledge along with variational techniques and Lagrangian methods in a nonlinear system of pde's, conversations will be directed towards a study on the evolution of an optical vortex in a finite nematic liquid crystal cell. Indeed, this study requires linearised stability analysis about the steady state for the given system to determined a relationship between the instability of an optical vortex and the minimum distance of approach to the boundary. Results from the mathematical study, show that the simple asymptotic approximations capture the amplitude of the optical vortex and its path towards its final steady state within a finite cell. The variational analysis results are compared to the full numerical solution for the non linear system. Good agreement is shown with all results.

###### Title

Fancy semigroups and nice C*-algebras

###### Abstract

A semigroup is a group without inverses. A C*-algebra is… well, more complicated! There is a natural way to construct a C*-algebra from a semigroup. We will describe a class of semigroups with a fancy name that give rise to nice C*-algebras .

###### Carole Birrell and Michael McCrae

Friday 4 May 2012  3:30pm

###### Talk 1

Preparing to Write a Mathematics/Statistics Thesis – MATH407/907 Research Methods

###### Abstract

Michael McCrae will introduce the issues and challenges associated with designing and writing mathematical and statistical theses that are covered in MATH907. Carole Birrell will then lead an inter-active discussion about what other issues they might want training in.

###### Talk 2

Becoming relevant at a local area: small area estimates from a state health survey

###### Abstract

Obtaining estimates of health risk factors at the local area is becoming more important than ever. NSW Health has collected data on health risk factors and health status across the state through a continuous population health survey since 2002, but it was designed to provide estimates for the state and for the health administrative units into which the state is split. The sample size of about 1000 observations per year from each administrative area is not sufficient to produce estimates at the local level. This talk will compare various model-based estimates obtained from applying small area estimation methods to the NSW population health survey data. It will focus on some of the issues faced when applying SAE methods to an ongoing survey.

James McCoy

Friday 20 April 3:30pm

###### Talk 1

Comparing evolving hypersurfaces

###### Abstract

We give a modern proof using the so-called "double coordinate" method that initially disjoint hypersurfaces remain disjoint during their common interval of existence when evolving by a given curvature flow. No special background is required for this talk. Talk 2: Fully nonlinear curvature flow of axially symmetric surfaces Speaker: Fatemah Mofarreh Abstract: The deformation of surfaces by speeds dependent on their curvature has a variety of mathematical and practical applications. I will briefly outline some of these applications before discussing some key ingredients in the analysis of the evolution of axially symmetric surfaces by fully nonlinear curvature-dependent speeds

###### Michael Whittaker

Friday 23 March 2012  3:30pm

###### Talk 1

The fractal dual of the pinwheel tiling

###### Abstract

A tiling of the plane refers to a covering of the euclidean plane by euclidean motions of a finite set of polygons that only intersect on their borders. I will introduce a selection of interesting tilings culminating in the pinwheel tiling, discovered by Conway and Radin. I will discuss a selection of interesting properties of the pinwheel tiling. I will then present fractals we discovered in the Pinwheel tiling along with a method for connecting the fractals to obtain a new tiling. This is joint work with Natalie Priebe Frank.

###### Talk 2

The notions of directed graphs and topological graphs

###### Abstract

First of all we define directed graphs and induce the C*-algebras of each graph. We will give some examples about graphs and algebras. Then we introduce topological graphs and try to "draw" one

Last reviewed: 28 October, 2013