School of Mathematics & Applied Statistics (SMAS)

# Seminars

### Applied mathematics/general seminars

Speaker: Ray Withers (ANU)
Time and Date: Friday 26 April 2013, 3:30pm
Room: 24-203

Title: Order and ‘disorder’, a chemist's view: what we know, what we don’t know and what we (often wrongly!) assume.

Abstract: In 1912 von Laue, Friedrich & Knipping first exposed a crystal to a beam of X-rays. The experiment was initially carried out in order to understand the nature of the radiation itself; instead, its real importance was the discovery of X-ray diffraction. In the same year, 1912, WL Bragg developed his famous law thereby making it possible to calculate the positions of atoms within crystals from the intensities of diffracted beams. The “diffraction” of X‑rays thus changed from the status of being a physical phenomenon to that of a tool for exploring the arrangement of atoms within crystals. The extraordinary success of X-ray crystallography ever since has led to the now largely “mature” science of crystallography. Like all successful disciplines, however, its very success inevitably led to the imposition of rigid “rules” as to what constitutes crystalline order and what doesn’t e.g. “ .. A unit cell of a crystal is a .. parallel-sided region .. from which the entire crystal can be built up by purely translational displacements ..” Shriver and Atkins, P66, 2009!! Wrong, as demonstrated by the (eventual) widespread acceptance of aperiodic/quasicrystalline order! Likewise, the direct observation of curved graphite planes in Transmission Electron Microscope (TEM) images of carbon support films in the 1960’s was ignored because “ .. lattice planes can’t curve ..”. Bye-bye the chance to discover bucky balls and bucky tubes much earlier than they were! In this contribution, a range of other fundamentalist type structural notions will be discussed ranging from the strange use of “nodal planes” when describing the molecular orbitals of 1-D “crystalline”, periodic ring molecules such as benzene or cyclopentadienyl to the question of why there is extensive notation describing “real”, but not “reciprocal”, space to the notion that a crystal structure refined from ISIS or synchrotron data with a good R‑factor is necessarily correct. The need to always keep thinking and to extend our ideas of what constitutes order to encompass whatever we experimentally encounter is still with us and continues to separate thoughtful structural chemists from handle‑turners. ‘Ordered’ crystalline materials are often far more subtle than the straitjackets imposed by crystallographic or chemical fundamentalism. Functionally useful materials (piezoelectrics, relaxor ferroelectrics, ionic conductors, solid solutions etc.), for example, are often modulated and frequently inherently flexible [1-3]. A detailed understanding of the structure, both average as well as local (on the relevant length and time scales) of such materials, is essential for an understanding of their properties and of methods to optimize and manipulate them. In this contribution, the results obtained from several such systems will be described including inherently Pb-free polar functional materials and the Li3xLn2/3‑xTiO3, 0.047 < x < 0.147, family of Li ion conductors. The local crystal chemistry underlying the inherent structural flexibility of these materials will be discussed along with the characteristic diffraction signatures of such behaviour.

_____________________

Speaker: Anne Thomas (University of Sydney)
Time and Date: Friday 19 April 2013, 3:30pm
Room: 24-203

Title: 3-manifolds, cube complexes and lattices

Abstract: A recent spectacular result in low-dimensional topology is that every closed 3-manifold has a finite cover which fibres over a circle. This was conjectured by Thurston in the 1970s, and proved by Agol in 2012, using geometric group theory, in particular group actions on cube complexes. I will explain some of the key ideas, and then give some applications to the study of lattices in locally compact groups.

_____________________

Speaker: Zhiyuan Liu (Monash University)
Time and Date: Friday 8 March 2013, 3:30pm
Room: 24.G03

Title: Optimal Toll Design Problem of Urban Congestion Pricing

Abstract: In a road transport network, the drivers’ route choice behaviour is un-cooperative, which would lead to an unwise use of the network and severe traffic congestions in some areas. Congesting pricing is one of the few instruments used by the transport authorities to properly adjust drivers’ route choice decisions. Based on given pricing locations, the Toll Design Problem aims to obtain the optimal toll pricing rate such that the total level of congestions in the network can mitigated. This presentation will first briefly review some congestion pricing practices in Singapore, London and Scandinavia. Then discuss about the modelling skills for the optimal toll deign problem. Subsequently, modelling for the Toll Design Problem for some newly proposed pricing schemes will be covered.

_____________________

Speaker: Lisa Clark (University of Otago)
Time and Date: Friday 22 February 2013, 3:30pm
Room: 24.204

Title: Spectral properties of C*-algebras associated to groupoids

Abstract: Groupoids appear in a number of different branches of pure mathematics. In operator algebras, we associate a C*-algebra to a grouoid so that properties of the algebra can be seen in propoerties of the groupoid. In this talk, I will begin by describing how a groupoid is a generalisation of the action of a group on a set. Then, I will describe how to associate a C*-algebra to a groupoid and demonstrate how spectral properties of the algebra correspond with topological properties of the groupoid.

This talk should be accessible to a general math audience.

________________________

Speaker: Dana Williams (Dartmouth College)

Time and Date: 3:30pm, Friday 30 November 2012 Room: 24-103

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.

___________________________

Speaker: Xiang Xu (Michigan State University)

Time and Date: 3:30pm, Friday 23 November 2012 Room: 24.103

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.

_________________________

Speaker: Andrew Francis (University of Western Sydney) Room: 15.206
Time and Date: 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.

_________

Speaker: Scott Morrison (Australian National University)

Time and Date: 3:30pm, Friday 26 October 2012
Room: 15.206

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.

______________

Speaker: Peter Kim
Room: 15.206
Time and Date: 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.

____________

Speakers: Ngamta Thamwattana and Alexander Gerhardt-Bourke (abstracts below).
Time and Date: 3:30pm Friday, 5 September 2012
Location: Room 15.206

Talk 1: Ngamta Thamwattana

Title: 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.

Talk 2: Alexander Gerhardt-Bourke

Title: 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.

____________________________

Day: Friday 3 August 2012
Location: Rm15.206
Time:  3:30pm

Talk: Directed graphs and their higher dimensional analogues
Speaker: Sam Webster

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.

Talk:  Voices in bounded soft media
Speaker: Luke Sciberras
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.

Day: Friday 1 June 2012
Location: Rm15.206
Time:  3:30pm

Talk : tba
Speaker: Aidan Sims and Andrew Holder
Abstract:

Day: Friday  18 May 2012
Location: Rm15.206
Time:  3:30pm

Talk : Fancy semigroups and nice C*-algebras
Speaker: Dr Nathan Brownlowe
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 .

Day: Friday  4 May 2012
Location: Rm15.206
Time:  3:30pm

Talk 1: Preparing to Write a Mathematics/Statistics Thesis – MATH407/907 Research Methods
Speaker: Carole Birrell and Michael McCrae
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
Speaker: Diane Hindmarsh
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.

Day: Friday 20 April 2012
Location: Rm15.206
Time:  3:30pm
Talk 1:Comparing evolving hypersurfaces
Speaker: James McCoy
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

Day: Friday 23 March 2012
Location: Rm15.206
Time:  3:30pm
Talk 1: The fractal dual of the pinwheel tiling
Speaker: Michael Whittaker
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
Speaker: Hui Li
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

Day: Friday 9 March 2012
Location: Rm15.206
Time:  3:30pm
Talk 1: Groups, trees, and operator algebras
Speaker: Jacqui Ramagge

Talk 2: Elaborate Distribution Semiparametric Regression via Mean Field Variational Bayes
Speaker: Sarah Neville

Speaker: Emeritus Professor Carl Chiarella, School of Finance and Economics, UTSTitle: The evaluation of American compound option prices under stochastic volatility and stochastic interest rates
Day: Wed 27 April 2011
Location: Access Grid Room (15.113)
Time:  12:30pm
Abstract: A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility process with a stochastic interest rate driven by a Cox-Ingersoll-Ross (CIR) process.  We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free boundary PDE problem which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the PSOR method.

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.

Speaker: Luke Sciberras

Title: Vortices 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.

Last reviewed: 26 April, 2013