Sajit is an international student from Nepal in his second year at Western Sydney University studying a Bachelor of Computer Science. He has previously completed a research project on astronomy which involved optimising radio telescope scanning patterns. His main areas of interest lie in data science, programming and statistics.

Apart from studying, Sajit enjoys reading, playing chess and photography.

Racism is prevalent in social media, but difficult to detect due to its language dependence. It is infeasible to use manual methods to detect racism in social media posts due to the large volumes of data, therefore automated methods are required. Unfortunately, the effectiveness of any automated method is heavily dependent on how we present the social media posts to the classifying machine. In this project, we will be examining the utility of word embedding methods word2vec and GloVe, for representing social media posts, to be used for classifying racism. Our research question is: ‘Do word embeddings trained on problem-specific text provide a more accurate representation than those trained using unspecific text?’. We will be using Google’s word embeddings for the unspecific representations and social media text for the specific representations.

James is currently in third year, majoring in Mathematics as part of the University of Western Australia’s exclusive Bachelor of Philosophy program. In the first year and a half at UWA he completed a research placement in graph theory with Prof. Gordon Royle. In the 2017-18 UK academic year, he spent a year abroad studying mathematics at University College London. Pure mathematics Honours awaits him in 2019.

James’ goal in life is to become a career researcher, lecturer and professional mathematician. So far, all areas of mathematics have been far too interesting for a particular favourite to emerge, except for a strict ban on doing applied mathematics. To help his quest to find his specialisation, his primary hobby is to collect, read and study mathematical textbooks.

Incidence geometry is the area of geometry only dealing with incidence (when a point lies on a line, etc), with no concept of angle, length or area. Of particular importance is the finite case: only finitely many points and lines. This area is particularly conducive to group theory by studying geometries with certain symmetry conditions. This project focuses on generalised polygons: finite incidence geometries whose structure generalises certain properties of the standard polygons. These were first defined by Jacques Tits in the appendix of a paper relating to the classification of Finite Simple Groups, where they play a surprising role. The symmetries of the generalised polygons are related in mysterious ways to the simple groups of lie type. There are many open questions about the types of group actions these groups can have on generalised polygons The research component of this project is two fold: 1: to learn about the various components of this topic, group actions, transitive and primitive groups, the theory and examples of generalised polygons, the structure of the finite simple groups and how they relate to each other. 2: Tackle the open question of whether there are “non-classical” generalised polygons on which some simple group of Lie type acts point and line primitively. So far there has been progress in finding restrictions on the type of groups and polygons for which there are point and/or line primitive actions. The aim of this project is to attempt to rule out specific examples as possibilities for giving a primitive action on any generalised d-gon, d>3.

Tom is a third-year student studying a Bachelor of Science in Mathematics. He intends to do honours in mathematics with a particular interest in Mathematical modelling in Biology. When away from studying he as a avid drum player and music fan.

The project will introduce new techniques for modelling neuron flows in the brain, using non-homogeneous Markov measures. This will allow the modelling of connected neurons with different parameters: by placing different weights on the individual neurons in the network of a Bratteli-Vershik diagram, we will provide a more realistic model of brain activity. A Bratteli-Vershik system (BV system) is an ordered graph whose vertices are organised in countably many layers, and with edges joining the layers. It is equipped with the Vershik operator, which is a generalisation of the odometer of classical ergodic theory, and a probability measure defined by weights on the edges, which can be understood as a non-homogeneous Markov measure. Dooley and Hamachi [DH] actually showed that every non-singular dynamical system is orbit equivalent to a Bratteli-Vershik system.

Daniel Condon is a third-year student finishing his Bachelor of Science in Analytics, with a major in financial mathematics. He has completed subjects in a range of fields including

mathematics, statistics and data science, where he has undertaken a number of data analytics projects. He has a keen interest in using mathematical and statistical tools to solve problems in data science such as improving machine learning techniques.

Artificial Neural Networks (ANNs) have become extremely effective in classification tasks involving large unstructured data sets such as in image recognition and natural language processing, however they are still outperformed by other machine learning techniques involving structured data. This project aims to explore Artificial Neural Networks in the context of structured datasets. The research component can be broken down into two sub-components which focus on the following questions:

- Can ANNs outperform traditional machine learning methods on structured datasets?
- How small can the structured dataset be before ANNs become ineffective?

Modern techniques such as entity embedding will be applied to the design of ANNs with the intent of creating an ANN which outperforms traditional machine learning techniques on structured data. Furthermore, this project will explore various sized datasets in an attempt to understand how small a structured dataset must be before ANNs become ineffective.

Rohin is currently studying the Bachelor of Advanced Science (Honours) at the University of Queensland. His interests lie mostly in the study of algebra and geometry. Throughout his degree, Rohin has gained valuable skills not only in his field of interest, but also in communicating to general and specific audiences. In particular, his work as a casual academic (tutor) for the University of Queensland has allowed him to impart his passion for the mathematical sciences to his fellow peers. In the future, he wishes to continue doing this for more of his fellows, whilst also undertaking his honours project in a similar field to this project.

The aim of this project is to study geodesics on low-dimensional homogeneous spaces, and in particular to prove the non-existence of clsoed geodesics for invariant Riemannian

metrics on some of the eight of Thurston’s three-dimensional model geometries. More specifically, we write the geodesic equation for arbitrary left-invariant metrics on one of the two simply-connected, non-abelian, solvable Lie groups which model the geometries: Nil and Solv (the Heisenberg Group H_3(R) and the group E(1, 1) of motions of the Minkowski plane, respectively). We also discuss the solutions of the differential equations thus obtained by exploiting the solubility of their Lie algebras.

Note: time permitting, we will also do the same for the universal cover of the special linear Lie group SL_2(R)

Jacquie is a second-year mathematics student at the University of Queensland. She enjoys all areas of pure mathematics, with a particular interest in the branches of mathematical

analysis. Upon completing her bachelor, Jacquie intends to do an honours project, continuing down the road of research into academia.

This project aims to further the understanding of how multiple solutions to elliptic geometric partial differential equations can be explicitly utilised to construct singular solutions to related problems. By applying a combination of variational and PDE methods, the student will develop techniques used in the analysis of constrained minimal surfaces, surfaces of prescribed curvature, and harmonic maps. This analysis will be conducted with a view to generalise the setting to that of Yang-Mills.

Jackson is a student at the University of Queensland, and is currently completing his third year of a Bachelor of Mathematics, majoring in pure mathematics. During this time Jackson has gained invaluable research skills, having completed a project in the area of graph theory, and plans to further these skills through his vacation research. He is interested in algebra and graph theory, and hopes to undertake an honours project related to these fields.

Since 2010, the SIMLESA program has been introducing sustainable agricultural technologies to farms in Southern and Eastern Africa, to increase crop yield and overall food security. Throughout the course of this program, surveys were conducted, obtaining data about which of the technologies had been adopted by each of the farms. The aim of this project is to examine a network which encodes the information obtained from these surveys. Using techniques from network analysis, the structure of the network will be investigated, which will provide insight into the effectiveness of this program.

Gavrilo Sipka is currently a mathematics student at the University of Queensland. He will be starting honours in the coming year. His interests lie in pure mathematics particularly abstract algebra, representation theory and number theory.

The project will be based around the study of quantum deformations of the universal enveloping algebra of a semi-simple Lie algebra depending on a parameter q. The project will focus on the quantum group of the special linear algebra sl(2). The project will go through understanding examples of fusion categories the come from the theory of quantum groups. We will study the representation theory of the quantum group associated to sl(2) in both the cases where the parameter q is not a root of unity and when it is a root of unity. We hope to understand how one can build interesting structures from the representation theory at roots of unity by using the theory of tilting modules. These ideas will be applied to construct semi-simple fusion categories from the representation theory when the parameter q is an odd root of unity. Lastly, the project will aim to look at the Lie super algebra osp(1|2) and investigate fusion categories that come from it’s quantum group. The key focus is to understand if one can obtain different fusion categories from the quantum groups of osp(1|2) and sl(2).

Vivien is a second-year student currently completing a Bachelor of Mathematics at University of Wollongong, with the intent to pursue Honours in 2020. Her research interests and experience are in mathematical modelling, particularly mathematical biology, though she is always looking to diversify her modelling experience and be exposed to as many

fields as possible. For her, the most incredible part about modelling is in how real-world phenomena can be represented and predicted mathematically; at times with startling

accuracy, even with relatively simple models. Modelling the baking of cake over the summer is a unique opportunity to become involved in the fascinating field of food engineering, and she is excited to develop new-found interest in this area.

Bread and bakery products have a worldwide revenue of US$272 billion. Baking involves several energy intensive processes, one of which is the heat and mass transfer of water.

When a cake bakes in the oven, its surface progressively dries, causing water and other species (e.g. CO2 produced by microorganisms everywhere in the product) to migrate from the wet core of the cake batter to the surface. By reducing final water content, the baker can reduce costs and ensure that produced goods are safe and desirable to the consumer.

The reaction engineering approach (REA) [1] is a simple yet effective drying model for heat/mass transfer of water. It captures the major physics of drying yet is relatively simple

in mathematical formulation, requiring a limited number of experiments to generate its parameters. On the other hand, existing empirical models fail to capture the major physics

of drying, and mechanistic models require too much data (due to too many parameters) for practical use in industry.

I aim to investigate the application of this emerging engineering approach to baking cake and its mathematical foundations. I also aim to analyse the derivation of model parameters from data and the effect of parameter uncertainty on predicted outcomes.

[1] Chen, X.D & Putranto, A., (2013). *Modelling Drying Processes: A reaction engineering approach*, Cambridge University Press, Cambridge.

Theresa O’Brien is a student in mathematics and statistics at the University of Wollongong. She first began as a student of sociology and linguistics before expanding her repertoire to mathematics and statistics in her second degree. She is primarily interested in mathematical modelling in the social sciences, but also has a keen interest in applied statistics and some fields of pure mathematics such as algebraic topology and noncommutative geometry. Applications of these to social science are also of interest because, she believes, there’s no such thing as overanalysis.

This project will investigate laughter propogation in a comedy audience through an agent-based modelling framework. Agent behaviour will be defined by a mixture of mathematical equations and stochastic processes in order to reflect the somewhat random, and intensely social, experience of comedy. Agents will be embedded in a weighted directed graph which represents people in spatial and social proximity through edge weighting, while the build up to a punchline, and the punchline itself, are environmental factors experienced by all agents at the same time.