S T U D E N TP R O J E C T S

AMSIVACATION RESEARCH SCHOLARSHIPS

2017-2018

2

CONTENTS

UNIVERSITY STUDENT PAGE

Federation University Tanya Pedersen 3 La Trobe University Patrick Adams 4 La Trobe University Yao Tang 5 Monash University Asama Qureshi 6 Monash University Drew Mitchell 7 Monash University Liam Hernon 8 Monash University Marcus Pensa 9 Monash University Michael Fotopoulos 10 Monash University Phillip Luong 11 Monash University Robert Hickingbotham 12 Monash University Sean Malcolm 13 Monash University Tim Banova 14 Queensland University of Technology Joel Rutten 15 Queensland University of Technology Jacob Ryan 16 Queensland University of Technology Steven Kedda 17 Queensland University of Technology Tamara Tambyah 18 Swinburne University of Technology Chrishan Christesious Aloysious 19 The Australian National University Dominique Douglas-Smith 20 The Australian National University Edric Wang 21 The Australian National University Jane Tan 22 The University of Adelaide James Beck 23 The University of Adelaide Michael Ucci 24 The University of Adelaide Miriam Slattery 25 The University of Adelaide Rose Crocker 26 The University of Adelaide Tobin South 28 The University of Melbourne Bing Liu 30 The University of Melbourne Benjamin Metha 31 The University of Melbourne Finn McGlade 33 The University of Melbourne Jiangrong Ouyang 34 The University of Melbourne Tianhe Xie 35 The University of Newcastle Riley Cooper 37 The University of Sydney Leo Jiang 39 The University of Sydney Ruebena Dawes 40 The University of Sydney Syamand Hasam 41 The University of Sydney Yilun He 42 The University of Sydney Yueyi Sun 43 The University of Western Australia Vishnu Mangalath 45 University of Wollongong Angus Alexander 46 University of Wollongong Lachlann O'Donnell 47 University of Wollongong Quinn Patterson 48

3

TANYA PEDERSEN

FEDERATION UNIVERSITY

BIOGRAPHY

Tanya Pedersen is a third-year Bachelor of

Information Technology student with Federation

University. Tanya’s primary area of interest is

Artificial Intelligence. She hopes to further explore

Artificial Intelligence over the next several years by

undertaking postgraduate research in the field.

DETERMINING AND EVALUATING BOUNDED ALGORITHMS FOR MOMAB

The project can be broken into four tasks, those being:

The formulation of different confidence intervals for Maximum Utility Loss in the Multi-

Objective Multi-Armed Bandits environment.

The development of a learning algorithm that terminates once a Maximum Utility Loss

bound is met.

The development of a learning algorithm that guarantees a MOPAC bound.

And finally, an empirical and theoretical comparison of our algorithms with those of

Auer et. al (2016).

SUPERVISORS

Dr Diederik Roijers, Dr Dean Webb, Associate Professor Peter Vamplew

4

PATRICK ADAMS

LA TROBE UNIVERSITY

BIOGRAPHY

I am Patrick Adams, currently completing my third

year in a Bachelor of Science, Master of

Nanotechnology double degree. In my time as a

student, I have completed many projects including

investigations of the UV laser beam writing,

simulation of x-ray beams, and reports on scientific

imaging techniques. Although most of my research has been predominately physics

based, my true passion is mathematics, having excelled in subjects of Linear Algebra,

Mechanics, Complex Analysis, and Statistical Computer Simulation. I am excited to

begin my first mathematics research project investigating planar graphic sequences,

as it will bring together my greatest passions, mathematics, arts, and computer

programming.

DETERMINING AND EVALUATING BOUNDED ALGORITHMS FOR MOMAB

A sequence non-negative integers greater than one is called graphic if there exists a

simple graph whose vertices have degrees in the sequence of interest. Characterizing

graphic sequences is given by the classical Erdos-Gallai Theorem, however there is

no indication as to whether the graph is planar or not. This project will involve finishing

up open cases in graphic sequence theorems and giving characterization for two-term

planar graphic sequences. This project will use graphic-theoretic, combinatorial

techniques and computer assisted approaches.

SUPERVISORS

Dr Grant Cairns, Dr Yuri Nikolayevsky

5

YAO TANG

LA TROBE UNIVERSITY

BIOGRAPHY

Yao is studying a Bachelor of Science degree with a

major in mathematics at La Trobe University. She

enjoys studying the general properties of various

algebraic structures such as groups, lattices and

vector spaces. An incorrigible miser, Yao

appreciates that doing mathematics require only a

pen, paper and a trash can. (She appreciates philosophy for similar reasons.)

Yao also has a liking of tabletop games, fantasy and world building. Giving a fictional

world drastically different properties than our own and seeing what follows can lead to

something beautiful.

ALGEBRA AND GEOMETRY OF QUANDLES

A quandle is a set with a binary operation satisfying certain axioms. They were

originally introduced to describe the algebra of Reidemeister moves in Knot Theory,

but exactly the same algebraic construction could be used for axiomatic description of

Riemannian symmetric spaces and so quandles can be viewed as “algebraic

symmetric spaces”. In the project, we aim to first study the known results, and then to

focus on understanding and classifying quandles of small cardinality and quandles

which are discrete analogues of k-symmetric spaces.

SUPERVISORS

Dr Grant Cairns, Dr Yuri Nikolayevsky

6

ASAMA QURESHI

MONASH UNIVERSITY

BIOGRAPHY

Asama has previously completed a degree in

software engineering and is now focused on

mathematics. He is interested in what can be

accomplished by combining the insights of

mathematics with the power of computing. His

current project extends what he is studying now in

functional analysis and partial differential equations, and he is excited about it as his

first exposure to mathematical research. Moving forward, there are many areas of

maths Asama is looking forward to exploring such as differential geometry, topology

and fractal geometry.

ESTIMATING CONSTANTS IN GENERALIZED WENTE-TYPE ESTIMATES

Wente’s classical estimate states that the solutions to some nonlinear elliptic problems

are more regular than it appears, owing to some compensation phenomena arising

from the special structure of the equations they satisfy. These estimates involve

constants that depend on the domain of the equation, and estimating these constants

are very important in practice. This project investigates new generalised Wente

estimates and aims at finding good upper bounds for the constants appearing in the

estimates.

SUPERVISORS

Dr Yann Bernard, Ting-Ying Chang

7

DREW MITCHELL

MONASH UNIVERSITY

BIOGRAPHY

Drew Mitchell is a third-year student in the Bachelor

of Science Advanced & Research (Honours) degree

at Monash University majoring in Mathematics and

Physics. He is interested in the areas of

computational mathematics, optimisation and

machine learning with a special focus on their

applicability to real world datasets. He will be entering into honours study in 2018 and

hopes to complete a project in the general area of numerical methods for big data

analytics. Drew was awarded a research first scholarship in 2015/2016 as part of

Monash Universities research first program and completed his project in experimental

optics. He worked for Monash University as a science student ambassador in 2016

and a project support officer for the school of physics in 2016/2017. He is currently

employed by Monash University as an ITAS (Indigenous Tutorial Assistance Scheme)

tutor for mathematics. Drew also undertook an internship with AON Hewitt in the

second semester of 2017 to gain experience in the industry of data analysis.

NUMERICAL OPTIMISATION METHODS FOR BIG DATA ANALYTICS

The data revolution is reshaping science, technology and business. Large-scale

optimisation is emerging as a key tool in extracting useful information from the deluge

of data that arises in many areas of application. This project will explore optimisation

methods for big data that include the stochastic gradient descent (SGD) method, and

use them to train models from machine learning such as logistic regression, with

applications in classification and recommendation systems. The aim of the project is

to learn about the algorithms and experiment with them, and we will investigate ways

to improve important algorithmic properties such as the speed of convergence.

SUPERVISOR

Professor Hans De Sterck

8

LIAM HERNON

MONASH UNIVERSITY

BIOGRAPHY

Liam Hernon is currently a third-year student at

Monash University, studying a science and

engineering double degree. Liam is passionate

about pure mathematics and believes the charm of

finding a simple solution to a complicated problem is

what makes it so appealing. He is particularly

interested in pursuing a research career, hoping to make contributions of his own.

Aside from mathematics, Liam enjoys playing guitar and chess in his spare time.

KNOTS, POLYNOMIALS AND TRIANGULATIONS

Many recent developments in knot theory have been driven by a web of conjectures

that relate quantum invariants and classical invariants. These conjectures are widely

considered to be immensely difficult and their verification on any interesting knot or

class of knots constitutes an important advancement of knowledge. We propose to

investigate one of these conjectures — the so-called Jones slope conjecture — on

some infinite families of knots.

SUPERVISORS

Dr Norman Do, Dr Josh Howie

9

MARCUS PENSA

MONASH UNIVERSITY

BIOGRAPHY

Marcus Pensa is a student in the Faculty of Medicine,

Nursing and Health Sciences with a concentration in

Biomedical Science and Mathematics at Monash

University. He is interested in mathematical

modelling of biological systems. Marcus is in his final

year of study in his Bachelor of Biomedical Science

degree, for which he has been awarded the Monash Scholarship for Excellence for

two consecutive years. In 2015, Marcus was recognised for his outstanding course

work in the University Mathematics subject Techniques for Modelling where he was

awarded the Highest Academic Performer. He has recently completed a summer

research project with the Australian Regenerative Medicine Institute (ARMI) where he

created a construct which is to be used for reprogramming adult marmoset (monkey)

cells into stem cells in a novel way. Marcus believes that research presents an

opportunity to combine his interests in cells, tissues, organisms and numbers.

AN INVERSE MODIFIED HELMHOLTZ PROBLEM FOR IDENTIFYING

MORPHOGEN SOURCES FROM SLICED BIOMEDICAL IMAGE DATA

One of the first patterning events in the development of multicellular organisms is the

production of a polar body from the symmetric Oocyte. The origin of these polar bodies

is poorly understood. The first sign that the polar body is going to be produced is the

asymmetric polymerisation of actin at the Oocyte surface. This can be seen from 2D

images of slices of the cell. The cause of this polymerisation and actin accumulation

is uncertain. A prevailing hypothesis is that a morphogen is produced that stimulates

the actin polymerisation. In this case, actin polymerisation should occur in locations of

high morphogen concentrations. Assuming the morphogen distribution in the cell can

be modelled with the modified Helmholtz equation, we will attempt to use the sliced

experimental images of actin to infer the source of morphogen production to aid in its

discovery.

SUPERVISOR

Dr Mark Flegg

10

MICHAEL FOTOPOULOS

MONASH UNIVERSITY

BIOGRAPHY

Michael is currently a student at Monash University

studying a Bachelor of Science/Bachelor of Music

double degree, majoring in both Pure Mathematics

and Jazz Composition, respectively. His

mathematical interests involve analysis and

differential geometry and through his undergraduate,

he is intent on further exploring these fields. He has recently participated in the

inaugural Simon Marais Mathematics Competition and was involved in a mathematics

enrichment program at the tutelage of Dr Angelo Di Pasquale throughout VCE. Having

always been fond of music, Michael is forever excited by the potential to unify his

musical and mathematical creativity in whatever his future studies may involve.

FUNCTIONALS OF HIGHER-ORDER DERIVATIVES OF CURVATURE FOR

SURFACES

The core aim of this project is to further the understanding of the Willmore energy,

which arises in conformal geometry, elasticity mechanics, general relativity, and string

theory. Using variational methods, the student will derive the Euler-Lagrange system

of equations for critical points of energy functionals involving higher-order derivatives

of curvature. With the help of Noether’s theorem, this system of higher-order equations

will be reduced to a larger system of PDEs of lower order, paving the way for a rigorous

analysis of the solutions of this system of equations. All which will be done is novel

and could potentially appear in print at a later time.

SUPERVISOR

Dr Yann Bernard

11

PHILLIP LUONG

MONASH UNIVERSITY

BIOGRAPHY

Phillip completing his fourth year in a double degree

studying the Bachelor of Science (Applied

Mathematics and Statistics) and Biomedical Science

at Monash University. He wishes to pursue a career

in mathematics that aims to have a significant

positive impact on the world.

Phillip has previously worked in research projects in range of different fields of maths,

including Infectious Disease Modelling in Public Health, modelling Traffic Flow on

Road Networks, and solving Nurse Rostering Problems in Operations Research.Aside

from studying, Phillip has interests in dance, board games and Japanese culture.

NUMERICAL OPTIMISATION APPLIED TO MONTE-CARLO ALGORITHMS FOR

FINANCE

The Least-Squares Monte-Carlo Algorithm is broadly used for pricing Bermudean

options. In this project we explore optimisation algorithms to extend this method to

representations using nonlinear basis functions. One of the keys to the success of this

approach is to solve efficiently a complex optimization problem, similar to those

encountered in neural networks.

SUPERVISORS

Professor Hans De Sterck, Associate Professor Gregoire Loeper

12

ROBERT HICKINGBOTHAM

MONASH UNIVERSITY

BIOGRAPHY

Robert is currently studying a Bachelor of Science

and Engineering at Monash University in Melbourne,

with an extended major in mathematics, and material

engineering. He has previously completed a

research project in mathematics which involved

looking at Lamplighter Random Walks. His main

areas of interest within mathematics is graph theory as well as optimisation. In his

spare time, Robert enjoys reading and studying the evidence for Christianity. He

intends on undertaking postgraduate studies in mathematics in order to pursue a

career in academia.

SPLITTING INTEGER LINEAR PROGRAMS WITH A LAGRANGIAN AXE

Lagrangian methods are great for splitting large real-world optimisation problems into

more manageable parts. However currently this is normally done manually. This

project will look for ways to analyse the mathematical structure of a collection of such

optimisation problems to try to automatically find good ways to split problems. The

project provides an opportunity to learn about advanced optimisation methods and

develop skills in computational mathematics.

SUPERVISOR

Professor Andreas Ernst

13

SEAN MALCOLM

MONASH UNIVERSITY

BIOGRAPHY

Sean just completed his second undergraduate year

at Monash University, studying science and majoring

in pure mathematics. His mathematical interests

include functional analysis, generating functions,

group theory, and more. In 2016, he also undertook

a project on Kakeya sets and their application to

Fourier multipliers, in particular the multiplier problem for the ball. He hopes to

undertake postgraduate studies in mathematics in the future.

PARALLELOGRAM POLYOMINOES, PARTITIONS AND POLYNOMIALS

The interface between mathematics and physics has proven to be a fertile area for the

discovery of new invariants in knot theory. One such example is the so-called 3d index,

which was discovered by theoretical physicists in 2011 and has since received a great

deal of attention from mathematicians. The basic building block of the 3d index is a

construction known as the tetrahedron index. From this object, one can derive

sequences of integers, whose terms are conjecturally positive and whose

combinatorial interpretations are currently unknown. We propose to prove these

positivity conjectures and seek the missing combinatorial interpretations, which may

shed new light on the 3d index.

SUPERVISOR

Dr Norman Do

14

TIM BANOVA

MONASH UNIVERSITY

BIOGRAPHY

Tim is a student at the School of Mathematical

Sciences at Monash University. Having just finished

his Bachelor of Science, he is keen to begin his

Honours year. In the future, he is interested in

continuing studying graph theory, combinatorial

geometry and other forms of combinatorial problems.

Outside of mathematics, Tim enjoys theatre, playing guitar and playing video games.

EXPLORING COMBINATORIAL GEOMETRY

Combinatorial geometry is the study of the combinatorial properties of arrangements

of geometric objects and is a rich source of simply stated but difficult open problems.

It combines elements of combinatorics, especially graph theory, with ideas from linear

algebra, convexity theory, topology and algebraic geometry. Together, we will select

an open problem, study its history and existing partial solutions in the literature, and

look for new ways to attack it.

Here is just one example: Given any drawing of the complete graph in the plane with

straight edges, how many colours are needed to colour the edges so that no two edges

of the same colour cross or share an endpoint?

Here is a second example: Consider a set of great circles arranged on the sphere so

that no three cross at a common point. This arrangement can be viewed as the drawing

of a planar graph whose vertices are the crossing points, and whose edges are the

arcs between crossing points. Since it is planar, it is 4-colourable. But can such graphs

also be 3-coloured?

SUPERVISOR

Dr Michael Payne

15

JOEL RUTTEN

QUEENSLAND UNIVERSITY OF

TECHNOLOGY

BIOGRAPHY

Joel is a third-year Bachelor of Mathematics student

studying at the Queensland University of

Technology, majoring in Applied and Computational

Mathematics, as well as Statistical Science. A Vice-

Chancellor’s Scholar, Joel has a keen interest in

sports and how Mathematics can be applied to the field, as well as a growing interest

in Mathematical Biology and Mathematics in Agriculture.

PATTERNS IN TURING PATTERNS: SEQUENTIAL GROWTH AND THE

INHIBITORY CASCADE

Certain repeating elements of the body, such as teeth, fingers, limbs and vertebrae,

are shown to follow the rule that the size of the middle element of a group of three is

the average size of the three elements [1]. This simple rule constrains how the relative

sizes of structures develop in the embryo and evolve over long periods of time. The

precise mechanisms that determine the number and size of repeating structures, such

as fingers and teeth, remain largely unknown. This project will develop mathematical

and computational models to investigate possible biological mechanisms of

sequentially patterned growth. These models will be based on reaction–diffusion

problems on growing domains [2, 3] and generalisations of Turing-like patterning

mechanisms.

References

[1] Kavanagh KD, Evans AR, Jernvall J (2007) Predicting evolutionary patterns of

mammalian teeth from development, Nature 449:427–433

[2] Simpson MJ, Landman KA, Newgreen DF (2006) Chemotactic and diffusive

migration on a nonuniformly growing domain: numerical algorithm development and

applications, J Comp App Math 192:282–300

[3] Buenzli PR (2016) Governing equations of tissue modelling and remodelling: A

unified generalised description of surface and bulk balance, PLoS ONE 11:e0152582

SUPERVISORS

Dr Pascal Buenzli, Dr Matthew Simpson

16

JACOB RYAN

QUEENSLAND UNIVERSITY OF

TECHNOLOGY

BIOGRAPHY

Jacob is currently in his third year of the Bachelor of

Mathematics Degree at QUT, majoring in Applied

and Computational Mathematics and Statistics. He

plans to graduate at the end of 2017 and begin an

Honours degree in the new year where he aims to

continue the research into modelling cell motion he began with his AMSI project.

Jacob is primarily interested in the applications of differential equations and has

previously completed a research project investigating solution methods to moving

boundary problems.

Outside of study, Jacob is interested in sports and movies.

REACTION DIFFUSION MODELS FOR CELL MOTION

In mathematical biology it is common to model cell motion using Fisher’s equation, a

second order PDE. The first part of this project involves reviewing the existing literature

for Fisher’s equation, particularly around travelling wave solutions and modelling the

spreading of cell populations. For the second part of the project, the student will

generalise Fisher’s equation to account for cells being in one of two phases of the cell

cycle. This will involve the implementation of numerical schemes to solve a coupled

system of nonlinear PDEs. If time permits, the student will apply the above results to

a case study, which will involve a two-dimensional migration and proliferation assay.

SUPERVISOR

Professor Scott McCue

17

STEVEN KEDDA

QUEENSLAND UNIVERSITY OF

TECHNOLOGY

BIOGRAPHY

Steven a QUT undergraduate student who studies a

double bachelor degree in mathematics and science,

majoring in applied and computational mathematics

and physics, respectively. Steven started his double

bachelor degree in 2014 and aims to complete his

undergraduate studies by the end of 2018, including an honours year. In Semester

One 2016, Steven received the Dean’s List Award for academic excellence. After

graduating, Steven intends to pursue a Ph.D in mathematics, where his specific fields

of interest are fractional calculus and numerical analysis.

Steven has previously undergone two summer research projects between academic

years at QUT. The first project investigated the (G’/G)-expansion method for solving

differential equations, the second project looked into the optimal control theory for

chemotherapy in HIV patients in order to determine the optimal administering rate of

chemotherapy treatment over time.

Steven’s non-academic interests include studying Chinese language and culture,

having studied Mandarin Chinese for over 2 years and soft-style application Tai Chi

for over four years. Steven has been an executive member of the Australia China

Youth Association student club for the past two years, being president of the QUT

chapter from August 2016 to September 2017.

PARAMETER ESTIMATION FOR THE FRACTIONAL ORDER NONLINEAR

DENGUE AND EPIDEMIC MODELS

In the last decades, dengue fever is a disease that has been found to cause problems

whose magnitude has increased dramatically. The World Health Organization (WHO)

recently stated that it is the most important arthropod-borne viral disease of humans.

Fractional derivatives epidemic systems have also been used to deal with some

epidemic behaviours. This proposal aims to carry out innovative and novel research

on developing efficient, robust, accurate computational models and parameter

estimation techniques for the fractional order nonlinear dengue and epidemic models

(FONDEM).

SUPERVISOR

Professor Fawang Liu

18

TAMARA TAMBYAH

QUEENSLAND UNIVERSITY OF

TECHNOLOGY

BIOGRAPHY

Tamara is in her third year of a duel Bachelor of

Mathematics and Bachelor of Science degree,

majoring in Applied and Computational Mathematics

and Physics, at Queensland University of

Technology (QUT). She is interested in multiple

areas of mathematics, namely applications of differential equations and linear algebra.

In 2015, Tamara completed a Science and Engineering vacation research project at

QUT where she explored mathematical models for droplet impaction. Completing this

project sparked her interest in research in applied and computational mathematics.

Tamara completed a semester abroad at the University of Leeds (UK) in 2016, where

she continued her studies in mathematics and physics.

While being a dedicated and high achieving student, Tamara is a voluntary Science

and Engineering mentor who provides peer tutoring.

INCORPORATING FUCCI TECHNOLOGY IN DISCRETE RANDOM WALK

MODELS OF COLLECTIVE CELL SPREADING

In this project we will develop lattice-based random walk models that incorporate cell

migration, cell-to-cell crowding, and we will represent the various ages of cells within

the cell cycle as a series of interacting subpopulations. Numerical simulations will be

used to explore how the population-level behaviour depends on the individual-level

mechanisms. To provide more formal insight, we will apply averaging arguments to

produce a series of new continuum reaction diffusion models that can be used to

describe experiments performed with FUCCI. These new mathematical models will

take the form of coupled nonlinear reaction diffusion equations, and we will explore

their solution using numerical approaches.

SUPERVISOR

Professor Matthew Simpson

19

CHRISHAN CHRISTESIOUS

ALOYSIOUS

SWINBURNE UNIVERSITY OF

TECHNOLOGY

BIOGRAPHY

I’m a hardworking, self-confident undergraduate

student who wants to attain a Robotics and

Mechatronics Engineering position in the future, to

use and develop my knowledge and skills while

taking up different challenges. To reach my goal I’m always in search of any good

opportunities in any form that would help me to develop new skills and improve the

skills I possess.

TIME DELAYS IN MODELLING THE BUBBLE CHAIN SYSTEM

Consider a bubble in compressible liquid. The well-known Rayleigh-Plesset equation

can be used to describe the oscillations of the bubble. When modelling coupled

bubbles or bubble-chain, coupling terms should be added showing the interaction

between bubbles. Since the sound speed is finite in compressible liquid, time delays

should be introduced to the coupling terms when investigating the interacting

behaviour [1]. The effect of time delay on dynamics of coupling bubbles or bubble

chain may be significant as in practical situations distances between bubbles may be

large enough [2] so that the effect from one bubble to another takes certain amount of

time. Analysis of time delay effects has attracted great attentions such as for systems

of two bubbles in [1,3] and for bubble chain in [4]. In these studies, authors assumed

the time delays were small enough so that Taylor expansions could be applied to terms

with time delays, which resulted in systems of ordinary differential equations, or they

just carried out numerical analysis for these systems. Different to their work, we will

treat the time delay as a parameter to analyse its effect.

In this project, we aim at investigating the effect of the time delays on dynamics of

coupling bubbles or bubble chain.

SUPERVISOR

Dr Tonghua Zhang

20

DOMINIQUE DOUGLAS-SMITH

AUSTRALIAN NATIONAL UNIVERSITY

BIOGRAPHY

Dominique has recently completed her second year

of undergraduate studies at the ANU. She is studying

a Bachelor of Science and a Bachelor of Music,

majoring in mathematics and piano performance.

Dominique has a strong interest in research and

would love to pursue a career in academia.

NONLINEAR UNIT HYDROGRAPH MODELS OF STREAMFLOW RESPONSE AND

WATER QUALITY

The aim of this project is to determine whether nonlinear unit hydrograph models will

offer better representations of flow peaks. The standard linear unit hydrograph offers

a poor reproduction of flow peaks for large events. Analysis of water quality

(concentrations and loads of various constituents) requires more accurate

representations of flow peaks, as these periods dominate the flow of constituents.

This project aims to develop and analyse a model of the nonlinear unit hydrograph.

This will improve the current rainfall-streamflow models and models of water quality.

SUPERVISOR

Associate Professor Barry Croke

21

EDRIC WANG

AUSTRALIAN NATIONAL UNIVERSITY

(UNIVERSITY OF SYDNEY)

BIOGRAPHY

Edric Wang is an undergraduate mathematics and

physics student at the University of Sydney where he

is a recipient of the Chancellor’s Award.

TENSOR NETWORKS AND CATEGORIES

Higher categories give an algebraic description of physics on spacetime. In the most

basic formulation, higher categories capture topological field theories only. Happily,

topological field theories are today important in condensed matter physics, providing

a mathematical formalism for studying topological phases of matter. Recent work in

condensed matter physics and quantum information theory has emphasised the study

of topological phases via tensor networks. This project will investigate the

mathematical connections between tensor networks, and higher categories. In

particular, we will study examples of reconstructing tensor categories from tensor

networks, along with reconstructing bimodules from 1-dimensional defects in tensor

networks.

SUPERVISOR

Associate Professor Scott Morrison

22

JANE TAN

AUSTRALIAN NATIONAL UNIVERSITY

BIOGRAPHY

Jane is currently a third-year student at the ANU,

where she is completing a Bachelor of Philosophy.

After spending a semester studying in Hungary, she

has been particularly interested in graph theory and

combinatorics, but is also keen on gathering ideas

and tools from a broad range of areas and being

exposed to as many different fields as possible. She looks forward to developing a

new-found interest in algebraic topology over the summer, as well as starting an

honours project in graph theory in 2018

SPECTRAL SEQUENCES IN ALGEBRAIC TOPOLOGY

In algebraic topology, homotopy groups are a generalisation of the fundamental group

to higher dimensions, and are of great theoretical importance. Unfortunately, they are

very difficult to compute. We consider instead the related but slightly more tractable

problem of computing stable homotopy groups. These were basically founded on

Freudenthal’s work and rose to significance after further development by Adams

through the introduction of his eponymous spectral sequence. In this project, we aim

to develop the tools needed to detail the process of computing stable homotopy groups

using spectral sequences, and apply this method following Adams’ work to concretely

compute the stable homotopy groups for certain spaces and spectra. In particular, this

will entail giving constructions of and applying the Serre and Adams spectral

sequences.

SUPERVISOR

Dr Vigleik Angeltveit

23

JAMES BECK

UNIVERSITY OF ADELAIDE

BIOGRAPHY

James is studying a Bachelor of Mathematical and

Computer Sciences at the University of Adelaide,

where he majors in both Statistics and Computer

Science. He is interested in Statistics, with a focus

on how it can be applied to medical research. He

plans to begin his Masters degree in 2019 to further

specialise in this field.

A STATISTICAL STUDY TO VALIDATE THE ICON-S STAGING SYSTEM FOR A

SOUTH AUSTRALIAN COHORT OF PATIENTS WITH HPV-POSITIVE

OROPHARYNGEAL SQUAMOUS CELL CARCINOMA

Oropharyngeal Squamous Cell Carcinoma is a type of cancer that affects the tissues

of the throat. The cancer is typically caused by either the HPV virus, tobacco or

alcohol. A new staging system was developed specifically for the HPV-positive cancer

recognising its different characteristics. Using data from a South Australian cohort of

patients with this type of cancer I will validate whether or not this new staging system

is more effective at predicting survival than the old system. This will be done using

various Survival Analysis techniques such as Kaplan–Meier curves and Cox

Proportional Regression.

SUPERVISOR

Professor Patty Solomon

24

MICHAEL UCCI

UNIVERSITY OF ADELAIDE

BIOGRAPHY

Michael is a 21-year-old-student, undertaking a

Bachelor degree in Science (physics) and

Mathematics at The University of Adelaide. Currently

in his third year of undergraduate study, Michael is

excited by the prospect of utilising mathematical and

statistical techniques to help understand and solve

real-world problems. Following Michael’s undergraduate study, he plans on

undertaking a postgraduate study in the areas of applied mathematics and statistics.

Aside from Michael’s studies, his interests lie in travelling, being outdoors, and

photography.

A STATISTICAL MACHINE LEARNING APPROACH TO IDENTIFYING

PROCALCITONIN AS A BIOMARKER FOR SEPSIS

Statistical machine learning methods will be applied to publicly available data in R.

Ultimately aiding the understanding and characterisation of the role of procalcitonin as

a diagnostic marker for sepsis.

SUPERVISOR

Professor Patty Solomon, Associate Professor John Moran

25

MIRIAM SLATTERY

UNIVERSITY OF ADELAIDE

BIOGRAPHY

Miriam Slattery graduated from high school in 2015

and has completed two years of a Bachelor of

Mathematical Sciences (Advanced) at the

University of Adelaide. She was the recipient of the

Marta Sved Scholarship for the highest-achieving

female student in Mathematics in 2016 and the Ann Coultas Prize for the first-year

student with the highest results in a statistics course in 2016. She has a keen interest

in mathematics, particularly mathematical modelling. Outside of academics, her

hobbies include facepainting and leading youth groups and youth camps.

OPTIMAL ANIMAL FORAGING IN A TWO-DIMENSIONAL WORLD

We aim to investigate a model for an animal searching for randomly located food in a

two-dimensional plane and seek solutions to give a minimum search time. We will do

this by extending analytical optimisation techniques used on a similar problem in one

dimension. We will also use simulations to find numerical solutions.

SUPERVISOR

Dr Giang Nguyen

26

ROSE CROCKER

UNIVERSITY OF ADELAIDE

BIOGRAPHY

Rose is a 4th year studying for concurrent degrees

in the Bachelor of Science (Advanced) and

Bachelor of Mathematical and Computer Science

programs at the University of Adelaide. She is

majoring in Physical Chemistry and Applied

Mathematics, with the aim of pursuing a Masters degree in an area related to Fluid

Mechanics and Differential Equations Analysis. In her spare time, she likes to cycle,

bush walk and draw.

EXTRACTING COHERENTLY MOVING FLOW STRUCTURES FROM FLUID

FLOWS

The equations governing the physics of fluids, with the exception of specific, simplified

cases, are notoriously intractable. Their solutions, however, are of great importance in

many fields of applied mathematics, including the modelling of geophysical flows,

oceanic currents and atmospheric dynamics. Consequently, it is often of interest to

analyse a flow’s coherent structure, rather than seek specific solutions to its governing

equations. Such analysis is of significance in many physical applications, such as in

examining the extent to which an oil spill will spread, the transport of air pollution or

heat flow in the atmosphere. In time-independent flows this is a fairly straight-forward

process, however; add time-dependence and identifying flow barriers becomes much

more challenging. This project will investigate the theory and application of

mathematical techniques capable of elucidating the coherent structure of time-

dependent fluid flows, including flow boundaries and transport across boundaries. In

particular, the Lagrangian Averaged Vorticity Deviation (LAVD) technique will be

employed to investigate the structure of classic vortical flows with important

applications in atmospheric and oceanic modelling, such as Rossby wave flow. LAVD

is a recent, lesser-studied and promising technique with great potential for the analysis

27

of vortical flows. The theory behind LAVD will also be examined to explore its

implications for physical models and its limitations. Time permitting, its application to

more complicated models, such as those incorporating three-dimensions, may also be

considered.

SUPERVISOR

Associate Professor Sanjeeva Balasuriya

28

TOBIN SOUTH

UNIVERSITY OF ADELAIDE

BIOGRAPHY

Tobin is a second-year student at the University of

Adelaide studying a Bachelor of Mathematical and

Computer Sciences. While at University, he has

developed a passion for Data Science, Big Data

Problems, Networks, and Machine Learning. Tobin enjoys spending his time working

on projects, usually building robots, with his mates and running the Mathematics

student society at University of Adelaide.

COLLABORATIVE NETWORK BASED CATEGORISATION MODELS

As a species, humans love to group things together. We group songs into genres,

folklores into categories and mathematical topics into disciplines. However, songs

often break genre conventions, folklores diverge from myth conventions, and

mathematical challenges draw from many different disciplines.

By using data sets to create a network of connections, the behaviour of these networks

can be examined. This project proposes the analysis of these networks, and it explores

if the current classifications are reflective of the actual clustering of the networks that

are created.

To achieve this, a variety of available data sets will be examined to construct networks

and develop new data-driven categorisation schemes based on observed network

properties, rather than arbitrarily assigned labels. An example of this process would

be to collect data from Spotify using an Application Programming Interface (API) to

build a collaboration network between artists, which will enable the graph properties

of this previously-unexplored network to be measured (e.g. degree distribution,

clustering, span, etc.), and then use the community structure of the network to develop

new genre classifications for musicians.

This project will explore the relationships between subjective classifications and the

community structure of the underlying networks. The research will attempt to answer

29

the questions, “How diverse are the people that contribute to ‘subreddits’ on Reddit?”,

or “Do genres mean anything in the modern age of musical collaboration?”, and more.

SUPERVISOR

Dr Lewis Mitchell, Professor Matthew Roughan

30

BING LIU

THE UNIVERSITY OF MELBOURNE

BIOGRAPHY

I am a student at School of Mathematics and

Statistics and also at the Faculty of Business and

Economics, University of Melbourne. My main

research interest is in the application of

Mathematics in Economics and Finance. However, I am new and thus open to every

possibility. I am currently working on a road pricing project, which involves both

stochastic modelling and market design. This summer, my supervisor Dr Laleh

Tafakori and I will research on a state space model to improve the current forecasting

of Realised Variance in financial markets.

FORECASTING OF REALISED VARIANCE MEASURE

Modelling- and forecasting-realised volatility plays an indispensable role for option

pricing, portfolio allocation and risk management. The existing models for realised

volatility may perform well in-sample but in general their out-of-sample forecasts are

often biased. We aim to build a model for realised volatility with improved forecasting

performance by accounting for the fact that that multivariate realised covariances are

only estimates of the true variance and by introducing time varying parameters. With

its more accurate forecasting, our model holds the promise to empirically more

accurate pricing models and improved financial decision-making. In estimating the

model parameters, we will apply the standardised self-perturbed Kalman Filter, which

performs very well in estimating state space models in terms of accuracy and

efficiency. After that, we will report the forecasting performance of the competing

models and look at the improvement in model fit of this new approach using other

benchmark models.

SUPERVISOR

Dr Laleh Tafakori

31

BENJAMIN METHA

THE UNIVERSITY OF MELBOURNE

BIOGRAPHY

Benjamin Metha is a student at the University of

Melbourne, having just completed a bachelor’s

degree of science majoring in pure mathematics, and

hoping to enrol in a Masters of Astrophysics. In 2016

he was awarded the Dixson Prize for pure mathematics, and in 2015 his name was

added to the Dean’s Honours list.

Benjamin has a keen interest in the medical sciences, as it allows him to apply the

skills he has learned in his undergraduate degree to help eliminate suffering around

the world. In 2017 he completed an internship at Stanford University, where he helped

improve image registration software developed for state-of-the-art ophthalmoscopes.

This year he is working with Dr. Jennifer Flegg, an expert in epidemiology from the

University of Melbourne, to study how malaria spreads through a population as well

as how drug resistance spreads amongst malaria parasites, in the hopes of developing

better treatment strategies for nations affected by malaria.

MODELLING THE SPREAD OF MALARIA AND ANTIMALARIAL DRUG

RESISTANCE

Malaria is one of the deadliest diseases in the world, causing approximately 429 000

deaths in 2015 [1]. It is only by having effective treatment methods that this disease

can be eliminated. However, the more often a drug is used, the more likely malaria

parasites will develop resistance to this drug. As the number of effective antimalarial

drugs on the market is limited, it is important to understand how drug resistance

spreads amongst malaria parasites, so this disease can effectively be combatted now

and in the future.

This project will compare a range of mathematical models for epidemics, using

sophisticated software [2] and historical data to simulate the spread of malaria through

a population and the subsequent emergence of drug resistance. Using these models,

32

different public health intervention strategies can be compared, to find out which

methods should be used to save the most lives in the long run.

[1] WHO Malaria fact sheet: http://www.who.int/mediacentre/factsheets/fs094/en/

[2] IDM Malaria Model:

https://institutefordiseasemodeling.github.io/EMOD/malaria/index.html

SUPERVISOR

Dr Jennifer Flegg

33

FINN MCGLADE

THE UNIVERSITY OF MELBOURNE

BIOGRAPHY

Finn is a third-year science major at Melbourne

University. He is currently completing a major in

mathematics and statics with a specialisation in pure

mathematics. Finn’s mathematical interests vary

across a wide range of specialisations. He enjoys learning ideas from the more

abstract areas of pure mathematics such as category theory and algebra, however he

is also interested in applications to physics and the world of probability theory. Finn’s

interests outside of mathematics include eating pasta and playing the bass.

A REFINED ALCOVE WALK MODEL FOR AFFINE SPRINGER FIBRES

Refined alcove path models are a recent development in combinatorial representation

theory, I propose to apply these models to attempt to study the combinatorics of the

affine Springer fibre in the case of the special linear group. This is work based on Arun

Ram’s refined alcove path model for the affine flag varieties. I have been attending a

series in which Arun has explained these models, and I hope to use the AMSI program

as an opportunity to build upon his work.

SUPERVISOR

Dr Yaping Yang, Professor Arun Ram

34

JIANGRONG OUYANG

THE UNIVERSITY OF MELBOURNE

BIOGRAPHY

Jiangrong Ouyang is a student in the Department of

Mathematics (majoring in Statistics) at the University

of Melbourne. His interests are around probability

and stochastic modelling. His current research lies in

branching processes for population modelling.

STOCHASTIC MODELS FOR POPULATIONS WITH A CARRYING CAPACITY

In this project, we will model the population of an endangered bird species, the black

robin.

The project will involve two main objectives which will be tackled using a combination

of simulation studies and theoretical developments.

Firstly, we will analyse different population-size dependent branching processes, and

develop parameter estimation methods to fit these models to the data. Secondly, we

are going to use this model to analyse demographic properties of the population.

These include the distribution of the time until extinction, the total progeny size and

the probability that the population becomes extinct before reaching a given size.

SUPERVISOR

Dr Sophie Hautphenne

35

TIANHE XIE

THE UNIVERSITY OF MELBOURNE

BIOGRAPHY

Tianhe Xie is a third-year student at the University of

Melbourne majoring in Neuroscience with a

concurrent diploma in Applied Mathematics. With an

ambition of unmasking the secrets of brain and

cognition, she is particularly interested in bioinformatics. So far Tianhe has obtained

research experience through participation in various projects in ecology and

mathematics, including building population model for koalas on French Island,

designing algorithm to find a heuristic allocation and location for cluster heads and

extracting and analysing geo-spatial data for Siberian cranes migration.

THE POPULATION HISTORY OF INDIGENOUS AUSTRALIANS: WHAT CAN THE

AVAILABLE GENETIC DATA TELL US?

In recent months, three major papers have appeared making strong claims about the

population history of indigenous Australians from genetic data: two appeared

in Nature. One of them used autosomal DNA, the others relying on only the

mitochondrial DNA. The claims from these papers appear to conflict with each other,

and many appear to be too precise to be adequately supported from genetic data

alone. Much of the data from these papers is available to other researchers, and other

data genetic resources are available for indigenous Australians and New Guineans.

In this project, I aim to apply more careful statistical inferences that may be able to

resolve some of the differences among these authors, and to distinguish claims that

are strongly supported from those that are more speculative.

REFERENCES

1) Malaspinas et al (2016) A genomic history of Aboriginal Australia, Nature 538, 207-14, 13 October

2016, doi:10.1038/nature18299

2) Nagle et al (2017) Mitochondrial DNA diversity of present-day Aboriginal Australians and implications

for human evolution in Oceania, Journal of Human Genetics 62, 343-353 (March 2017) |

doi:10.1038/jhg.2016.147

36

3) Tobler et al (2017) Aboriginal mitogenomes reveal 50,000 years of regionalism in

Australia, Nature doi:10.1038/nature21416

SUPERVISOR

Professor David Balding, Dr Jennifer Flegg

37

RILEY COOPER

THE UNIVERSITY OF NEWCASTLE

BIOGRAPHY

Riley Cooper is an undergraduate student in the

School of Mathematical and Physical Sciences at the

University of Newcastle, studying a Bachelor of

Mathematics degree with specialisation in Applied

Mathematics and Statistics. He is interested in Applied Mathematics with focuses on

Optimisation, Programming and Computation and Statistics with focuses on Bayesian

Analysis, Markov Chains and Data Science. Flexibility of the Bachelor of Mathematics

degree has allowed Riley to study a range of topics in Pure Mathematics on top of the

Applied Mathematics and Statistics Majors. Riley has also established programming

skills in different languages in relation to his university study. By being placed on the

Faculty of Science and Information Technology Commendation List for every year of

tertiary study to date, Riley has proven strong academic results. Riley was granted the

Faculty of Science and Information Technology Summer Vacation Scholarship in 2016

and was able to pursue his interest in Mathematical Research. Under the supervision

of Dr Thomas Kalinowski, Riley completed a research project titled “Allocation of

Indivisible Goods”. Studying abroad at the University of Leeds in 2017 gave Riley the

opportunity to experience university life in a different country, travel, and build many

personal skills. Riley intends to complete an Honours degree in Applied Mathematics

or Statistics and to then to pursue work and/or graduate study.

LOT SIZING ON A CYCLE

Production planning and scheduling problems are a key component in many supply

chains. A recurring model in these problems is the multi-item lot sizing model in which

a schedule of production is determined for each item being produced so that the

demand for each item is satisfied subject to constraints on production, inventory and

the operation of the machinery. In this project, we will investigate a variant of the

classical deterministic single-item lot sizing problem in which the underlying network

38

is a cycle. Such a variant is motivated by strategic production planning and scheduling

problems in which it is often convenient to assume that the planning horizon wraps

around on itself, thereby eliminating the need to specify boundary conditions and

avoiding possible end effects. Such an approach can be viewed as a form of steady

state model.

In this project we will introduce the single-item lot sizing problem on a cycle. We will

propose a mixed-integer programming formulation for the problem, explore the

structural properties of the optimal solutions, and use them to establish the

computational complexity of the problem and develop efficient algorithms for its

solution. Finally we will investigate the polyhedral structure of the convex hull of the

set of feasible solutions to the problem and propose extended formulations and strong

reformulations for the problem.

SUPERVISOR

Dr Hamish Waterer

39

LEO JIANG

THE UNIVERSITY OF SYDNEY

BIOGRAPHY

Leo is currently an undergraduate student at the

University of Sydney with majors in mathematics and

chemistry. His mathematical interests include

category theory, knot theory, and ergodic theory, and

he would like to know more about representation theory. In 2018 he is planning to

pursue Honours in pure mathematics.

NIEMEIER LATTICES AND HOMOLOGICAL ALGEBRA

The goals of this project are:

– to define and classify Niemeier lattices as they arise from gluing root lattices

– to categorify root lattices, that is, present them as Groethendieck groups of module

categories

– to understand the obstacles in lifting gluing constructions to the categorical level

(original research)

SUPERVISOR

Dr Zsuzsanna Dancso

40

RUEBENA DAWES

THE UNIVERSITY OF SYDNEY

BIOGRAPHY

Ruebena Dawes is from Sydney, Australia, and is

due to complete a Bachelor of Science (Advanced

Mathematics) at The University of Sydney in 2017,

with majors in applied mathematics and

biochemistry. She began her degree with a broad interest in mathematics, and

although she retains a deep appreciation and wonder for pure mathematics, she has

decided her passion is in applying mathematics and mathematical principles to issues

in the medical sciences. In addition, in the past year she has been learning a lot about

computer science and big data and is excited to begin a career at the intersection of

these three disciplines.

MATHEMATICS IN MEDICINE: USING OPTIMISATION TO IMPROVE CANCER

TREATMENT

Effective radiotherapy is dependent on being able to (i) visualise the tumour clearly,

and (ii) deliver the correct dose to the cancerous tissue, whilst sparing the healthy

tissue as much as possible. In the presence of motion, both of these tasks become

increasingly difficult to perform accurately – increasing the likelihood of incorrect dose

delivered to cancerous tissue and exposure of healthy tissue to unnecessary radiation,

causing adverse effects. This project will develop mathematical optimisation tools to

improve the quality of diagnostic images and treatment accuracy, and requires some

programming experience.

SUPERVISOR

Dr Michelle Dunbar

41

SYAMAND HASAM

THE UNIVERSITY OF SYDNEY

BIOGRAPHY

Syamand Hasam is a 2nd-3rd year undergraduate

student at the University of Sydney studying a BSc

(Advanced) double majoring in Mathematics and

Statistics. He also holds a completed Bachelor of

Computer Science and Technology from the University of Sydney. Academic interests

are still wide ranging across pure and applied mathematics, theoretical computer

science, statistics and the application of such in the fields of medicine and biology.

WHEN IS TARGET-DECOY COMPETITION VALID?

In a problem to do with mass spectrometry analysis, we wish to investigate whether

recent methods in controlling the FDR (False Discovery Rate) for predicting the best-

scoring-peptide match, are justified in their assumptions by looking at these methods

in relation to real data, and questioning the assumptions used.

SUPERVISOR

Associate Professor Uri Keich

42

YILUN HE

THE UNIVERSITY OF SYDNEY

BIOGRAPHY

Yilun He is a BSc (Adv. math) student in University

of Sydney. He is studying statistics and computer

science. He specializes in the study of hypothesis

testing and computer algorithms.

At the moment Yilun receives a scholarship from Victor Chang Cardiac Research

Institute and is working on a individual project.

He also received a summer scholarship from Data61 and commenced research on

interactive theorem prover with functional programming implementation. In addition,

he received a summer research scholarship from department of mathematics and

statistics of University of Sydney.

He is interested in bioinformatics, financial mathematics and statistics.

CONDENTLY CONTROLLING THE FALSE DISCOVERY PROPORTION

The aim of this project is to explore the property of false discovery rate (FDR): the

expected percentage of true null hypotheses among all the rejected hypotheses. FDR

is widely used in modern large hypothesis testing. A deeper understanding in the

concept is very important to the correctness of these inference.

SUPERVISOR

Associate Professor Uri Keich, Kristen Emery

43

YUEYI SUN

THE UNIVERSITY OF SYDNEY

BIOGRAPHY

Yueyi Sun is currently a third year Science

student in the Mathematics and Statistics,

at The University Of Sydney. She will

graduate in Dec. 2017 with a Bachelor of

Science (advanced mathematics) and

minor in IT. She is interested in financial

mathematics and risk management. More specifically, her work examines games

theory.

CAN WE MAKE MONEY USING THE GAMES THEORY?

The rst part of this project will be devoted to learning basic concepts of game theory.

This will require reading selected sections from [1]. An emphasis will be put on Nash

equilibria and their properties. Nash equilibrium is a very nice mathematical idea but it

leads to many mathematical diculties and it is far from obvious that it describes

behaviour of real economic agents [4]. It is usually not unique and very unstable and

these properties undermine its applicability. On the other hand it is very conservative

towards risk taking while real agents are typically much more optimistic. We will learn

about some modications of the concept of Nash equilibrium, such as maxmin

strategies [5] or evolutionary games, [4]. An associated concept of (bounded)

rationality will also be studied. We will follow here the classical works by Aumann,

Simon and Myerson.

In the second part of the project we will study some modern extensions of the game

theory developed for situations when the number of players (economic agents) is very

large. The starting point for this new development is the assumption that the economic

agents are “exchangeable”, that is, the joint probability distribution of the positions of

all players does not change after arbitrary permutation of the players. Then an

intractable (high-dimensional) problem of nding the Nash equilibrium can be reduced

44

to a game against a single opponent representing the mean behaviour of the

population of players. This approach has been borrowed from the mean eld theory in

statistical physics but the optimisation problem brings new mathematical questions

and a wide range applications in economics, mathematical nance, biology and social

sciences for example in modelling crowd behaviour). It is known as the mean eld

games (MFG) approach (or theory).

In this project we will focus on some recent attempts [2, 3] to use the MFG theory in

order to describe how the market equilibrium arises from actions of a large (innite)

number of economic agents. It turns out that this approach provides important insights

into the high frequency trading and predatory economic behaviour. We will concentrate

on the single-queue model for the price formation in high frequency trading, as

presented in Section 3 of [3]. The main simplifying assumption made in this section is

that the process of arrivals of traders is described by an exogenous Poisson process

with a xed intensity . We will investigate a situation, when the intensity (x) depends on

the size x of the queue. To this end, we will try to modify arguments presented in [3].

Since in [3] the innitesimal arguments at equilibrium are used to derive the basic mean

eld game equation, we expect that such an extension is achievable. In the project we

still assume that the intensity function x ! (x) is exogenously given but our assumption

that depends on x is a modest attempt to take into account the fact that behaviour of

the traders depends on the state of the market. An interesting question how this

function arises as part of the equilibrium is beyond this project.

References

[1] Aliprantis, Charalambos D.; Chakrabarti, Subir K. Games and decision making. OUP, 2011

[2] Carmona R.; Webster K. High Frequency Market Making Making, https://arxiv.org/abs/1210.5781

[3] Lachapelle, Aime; Lasry, Jean-Michel; Lehalle, Charles-Albert; Lions, Pierre-Louis. Eciency of the

price formation process in presence of high frequency participants: a mean eld game analysis. Math.

Financ. Econ. 10 (2016), no. 3, 223-262

[4] Mailath, George J. Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory.

Journal of Economic Literature 36, No. 3 (Sep., 1998), pp. 1347-1374

[5] Pruzhansky, Vitaly. Some interesting properties of maximin strategies. Internat. J. Game Theory 40

(2011), no. 2, 351-365

SUPERVISOR

Professor Beniamin Goldys

45

VISHNU MANGALATH

THE UNIVERSITY OF WESTERN

AUSTRALIA

BIOGRAPHY

Vishnu Mangalath is a Bachelor of

Philosophy student from the University of

Western Australia majoring in Mathematics

and Physics. He has a wide range of

interests in pure mathematics and physics,

particularly, algebraic topology and geometry, statistical mechanics and quantum

mechanics. He will be completing his honours in mathematics in 2018 in pure

mathematics.

HOMOLOGY AND COMPUTATIONS FROM NERVES

This project will start by investigating the basics of simplicial homology theory, a well-

established feild of algebraic topology, up to and including the Mayer-Vietoris exact

sequence. During this investigation, the student will gain the required back- ground for

further investigation, such as constructing simplicial complexes from the nerve of an

open cover of a topological space.

The research component will predominantly involve calculating the homology groups

of the nerve of an open cover found from experimental data. For example, this data

may be points from the state space of some unknown dynamical system. From this

we can take an open cover of this data and therefore construct a simplicial complex

via the nerve. Calculating the homology groups of these simplicial complexes will give

insight into the shape of the underlying state space.

SUPERVISOR

Professor Lyle Noakes

46

ANGUS ALEXANDER

UNIVERSITY OF WOLLONGONG

BIOGRAPHY

Angus is currently in his third year of a

double degree studying mathematics and

physics. He intends to pursue honours in

maths in 2019. His main interests are

subjects related to mathematical physics, in

particular differential geometry and

operator theory.

DIFFERENTIAL OPERATORS ON MANIFOLDS AND APPLICATIONS IN PHYSICS

The project will begin by developing the theory of differentiable operators on manifolds.

It will then apply the theory to problems in relativity, especially the index of the

relativistic Dirac operators on cylinders.

SUPERVISOR

Associate Professor Adam Rennie, Professor Alan Carey

47

LACHLANN O’DONNELL

UNIVERSITY OF WOLLONGONG

BIOGRAPHY

Lachlann O’Donnell is a student at the

University of Wollongong undertaking a

Bachelor of Mathematics. He graduated in

2017 and is doing an honours project in

geonetric analysis in 2018. His interests lie

in the areas of Differential Geometry,

Topology and Analysis with particular emphasis on Differential Geometry.

FULLY NONLINEAR CURVATURE FLOW

The area of curvature flow was developed to deal with problems that arise in geometry,

for example the Poincare conjecture was resolved through the use of Ricci flow. The

project aims at discussing specific types of curvature flows i.e. contraction and

expansion flows, culminating in considering the cases of fully nonlinear curvature

flows.

SUPERVISOR

Dr Glen Wheeler

48

QUINN PATTERSON

UNIVERSITY OF WOLLONGONG

BIOGRAPHY

Quinn has just completed his third

undergraduate year in a bachelor of

advanced mathematics at University of

Wollongong. Quinn will be completing a

project on differential operators on

manifolds and positive scalar curvature

alongside fellow student Angus Alexander under supervisors Adam Rennie and Alan

Carey.

DIFFERENTIAL OPERATORS ON MANIFOLDS AND POSITIVE SCALAR

CURVATURE

The project will begin by developing the theory of differential operators on manifolds.

The research component will be applying the theory to the effect of curvature on the

index of the Hodge De Rham operator, namely the Euler characteristic.

SUPERVISOR

Associate Professor Adam Rennie, Professor Alan Carey