Project List
Faculty of Science
School of Mathematics and Statistics
MATH01: New data science approaches for single cell
spatial genomics
Recent developments in single cell RNA-sequencing and spatially resolved genomics (e.g. seqFISH, 10X Visium) have resulted in immense datasets corresponding to hundreds of thousands of observed cells and thousands of measured features. The overarching goal is to develop new data science approaches to addressing questions in biology and create new algorithms for understanding these data. There are opportunities to build capacity in terms of computational modelling, effective data visualisation and interaction, and software scalability.
Supervisor(s): Shila Ghazanfar
Prerequisites: DATA2002/DATA2902
Maximum number of places available: 4
Project Location: Camperdown (Carslaw, CPC)
Final
assessment: Project
presentation, 5-10 minutes
Contact: mailto:shila.ghazanfar@sydney.edu.au
MATH02: Scaling laws in Urban data from Australia.
This project will combine mathematical models, computational techniques, and statistical methods to investigate the existence of universal statistical laws in data of Australian cities. The most famous of such as laws is the so-called Zipf's law of cities, and the goal is to investigate the dynamics of the population size in Australian cities that resulted in its two largest cities having similar sizes. The project will also consider urban-scaling laws, expanding and building on the models and results of Ref. [1], and considering new types of data (e.g., census, geo-located twitter data) and mathematical methods (e.g., new spatial interactions, new MCMC inference methods).
Supervisor(s): Eduardo Altmann
Prerequisites: Knowledge of a programming language and at least basic knowledge of Python. First year Calculus and Statistics or Data Science.
Maximum number of places available: 2
Project Location: Camperdown Campus, Carslaw Building
Final
assessment: Project
Presentation, 5 – 10 minutes
Contact: mailto:eduardo.altmann@sydney.edu.au
MATH03: Exploring Statistical Models for Animal
Behavior Analysis.
This project offers a unique opportunity to decipher the underlying patterns and motivations driving animals' actions during the warm months. By employing cutting-edge statistical techniques, you will uncover hidden insights from observational data, shedding light on factors influencing animal behaviour. Immerse yourself in the natural world while honing your analytical skills and contributing to a deeper understanding of the fascinating behaviors that unfold in the animal kingdom during summertime.
Supervisor(s): Clara Grazian
Prerequisites: Statistical theory (at least STAT2011)
Maximum number of places available: 1
Project Location: Sydney, Camperdown Campus
Final
assessment: Project
report, 1-2 pages
Contact: mailto:clara.grazian@sydney.edu.au
MATH04: AI and Natural Language Processing for
Healthcare.
Clinical notes contain key information about patients, but they are difficult to interpret. The style of writing is a challenge even for large language models (LLMs) like ChatGPT, because the writing is unlike the training data for LLMs (online text and books). This project is about developing an AI-based system for clinical coding: identifying key information in clinical notes.
Supervisor(s): Jonathan K. Kummerfeld
Prerequisites: Experience in Python (either through first year CS units or extensive experience elsewhere)
Maximum number of places available: 2
Project Location: Camperdown campus
Final
assessment: Project
presentation, 5-10 minutes
Contact: mailto:jonathan.kummerfeld@sydney.edu.au
MATH05: AI and Natural Language Processing:
Collaborative Intelligence for Crowdsourcing.
Many AI systems rely on labelled data for training. Creating those resources is usually a laborious process performed by experts. For some tasks, methods have been developed for non-experts to label data, e.g. for identifying objects in images. This project aims to push the boundaries of what non-experts can do by taking advantage of AI. One directions is an adaptive labelling system, where people do most of the work at first, but then the system automatically shifts over time to use more AI input and less human input. The other direction is to create a human-AI collaborative system that can do perfect real-time speech recognition.
Supervisor(s): Jonathan K. Kummerfeld
Prerequisites Experience in Python (either through first year CS units or extensive experience elsewhere)
Maximum number of places available: 2
Project Location: Camperdown campus
Final
assessment: Project
presentation, 5-10 minutes
Contact: mailto:jonathan.kummerfeld@sydney.edu.au
MATH06: Data-intensive science to understand the
molecular aetiology of disease.
Biotechnological advances have made it possible to monitor the expression levels of thousands of genes and proteins simultaneously promising exciting, ground-breaking discoveries in complex diseases. This project will focus on the application and/or development of statistical and machine learning methodology to analyse a high-dimensional biomedical experiment. Our lab works on projects spanning multiple diseases including melanoma, acute myeloid leukemia, cardiovascular disease, organ transplant, multiple sclerosis and HIV.
Supervisor(s): Ellis Patrick
Prerequisites: Completion of DATA2X02 or equivalent
Maximum number of places available: 4
Project Location: The School of Mathematics and Statistics (Carslaw building) and/or The Westmead Institute for Medical Research and/or remote.
Final
assessment: Project
presentation, 5-10 minutes
Contact: mailto:ellis.patrick@sydney.edu.au
MATH07: Analytics for Randomized Controlled Trials in
Hypertension Management.
This project aims to use longitudinal blood pressure (BP) progression data sets to make the optimal treatment decision. The BP progression is modeled by a Brownian motion. We will use simulation to estimate the potential impact of the model.
Supervisor(s): Qiuzhuang Sun
Prerequisites: Comfortable with computers and statistical analysis; familiarity with R or Python
Maximum number of places available: 5
Project Location: Sydney
Final
assessment: Project
report, 1-2 pages
Contact: mailto:qiuzhuang.sun@sydney.edu.au
MATH08: Post-quantum cryptography.
Quantum computers are expected to break currently used secure public-key algorithms. This project will investigate ideas underlying proposed new "quantum-proof" algorithms related to mathematical structures.
Supervisor(s): Nalini Joshi
Prerequisites: Interest in symbolic mathematical computation, second-year mathematics units, interest in learning magma and cryptography.
Maximum number of places available: 2
Project Location: University of Sydney, Camperdown campus
Final
assessment: Project
report, 1-2 pages
Contact: mailto:nalini.joshi@sydney.edu.au
MATH09: Software development for measurement error
correction.
Measurement error is ubiquitous in big data and can seriously distort relationships among variables in the dataset. Hence, it is imperative to correct measurement errors to gain appropriate insights from the data. A recently developed method, called simulation-selection-extrapolation, is able to correct measurement errors in a wide range of settings, especially in settings with a large number of variables in the dataset. The project aims to develop statistical packages for this methodology, making it more accessible to a wide range of audiences and practitioners. Through the project, students will gain knowledge about advanced statistical modeling and have experience developing high-quality software.
Supervisor(s): Hoang Linh Nghiem
Prerequisites: Skills: Proficient with programming in R or Python; intermediate knowledge about statistical modeling, preferably having taken STAT3022 and/or STAT/DATA3888 or an equivalent unit.
Maximum number of places available: 2
Project Location: Sydney or online
Final
assessment: Project
report, 1-2 pages
Contact: mailto:linh.nghiem@sydney.edu.au
MATH10: An approximate model of the Levitron.
The Levitron is a magnetic symmetric top, that can levitate while spinning. There is an exact theory for it's motion, and various approximate simpler models. The goal of this project is to derive an approximate simpler model from the exact model, and compare them analytically and with numerical experiments.
Supervisor(s): Holger Dullin
Prerequisites: Ideally students will have done MATH3977
Maximum number of places available: 2
Project Location: Carslaw Building Camperdown
Final
assessment: Project
report, 1-2 pages
Contact: mailto:holger.dullin@sydney.edu.au
MATH11: Methods towards precision medicine.
Over the past decade, new and more powerful -omic tools have been applied to the study of complex diseases such as heart attacks and generated a myriad of complex data. However, our general ability to analyse this data lags far behind our ability to produce it. This project is to develop computational methods that help identify disease pathways and deliver better prediction of outcomes. This project could also investigate whether it is possible to establish associations between features extracted from imaging data and cellular measurements from a large cohort of individuals.
Supervisor(s): Jean Yang
Prerequisites: Comfortable with computers and statistical analysis, familiarity with R, assume DATA2002 knowledge.
Maximum number of places available: 4
Project Location: CPC or Carslaw, Camperdown
Final
assessment: Project
report, 1-2 pages
Contact: mailto:jean.yang@sydney.edu.au
MATH12: Imaging-omics for precision medicine in CAD.
In the ongoing battle against diseases like heart attacks, medical technology has seen significant advancements, equipping clinicians with innovative diagnostic tools. Alongside this, there's a growing demand for the application of machine learning techniques to extract meaningful insights from this data. The aim of this project is to explore potential associations between features derived from imaging data and cellular measurements across a vast number of individuals using machine learning approaches. Ultimately, this could lead to the identification of key features from either imaging or multi-omics modalities, enhancing our ability to predict Coronary artery disease (CAD) outcomes.
Supervisor(s): Jean Yang
Prerequisites: Comfortable with computers and statistical analysis, familiarity with R, assume DATA2002 knowledge.
Maximum number of places available: 4
Project Location: CPC, Camperdown
Final
assessment: Project
report, 1-2 pages
Contact: mailto:jean.yang@sydney.edu.au
MATH13: Translation surfaces and origami.
Translation surfaces are surfaces obtained by gluing sides of polygons together with translations. They hold a unique position at the crossroads of topology, geometry and dynamics, and are related to the study of billiard trajectories.
The study of the space of these surfaces, their moduli space, is a rich area of current research.
Questions include understanding deformations of these surfaces: can one continuously deform a given translation surface into another? Can this be achieved by applying two-by-two matrices on the polygons?
Origami are special cases of translation surfaces. They are surfaces obtained by gluing unit squares along their edges. Many questions then acquire a combinatorial flavour and are related to the study of the symmetric group.
The aim of this project is to get a glimpse of this research domain by focusing on these simple objects that still hold many mysteries.
Supervisor(s): Thomas Le Fils
Prerequisites: Linear algebra (MATH2922 or MATH2022). Desirable knowledge of basic group theory (symmetric group).
Maximum number of places available: 2
Project Location: University of Sydney (Quadrangle, SMRI)
Final
assessment: Project
presentation, 5-10 minutes
Contact: mailto:thomas.fils@sydney.edu.au
MATH14: Identifying gaps in curriculum alignment.
While robust curriculum design seeks for the constructive alignment of all learning activities and assessments, it is easy for gaps to emerge between what is explicitly taught and assessed, especially in a dynamic environment where there is a large cohort, team teaching and a culture of continual improvement. How can we identify possible discrepancies in curriculum alignment?
Supervisor(s): Di Warren
Prerequisites: HD/D in DATA1001/1901; Or CR+ in DATA2002/2902
Maximum number of places available: 2
Project Location: University of Sydney, Camperdown
Final assessment: Project report, 1-2 pages
Contact: mailto:diana.warren@sydney.edu.au
MATH15: What are isomonodromic
deformations?
Some differential equations have the incredible property that their solutions can be fully determined by the associated geometry. In this project you will first explore the cubic surfaces related to such differential equations. Then we understand how to deform the equations such that the cubic surface remains invariant. Such deformations are called isomonodromic deformations, and have far reaching implications in mathematics and physics.
Supervisor(s): Harini Desiraju
Prerequisites: Basic knowledge of complex variables in needed.
Maximum number of places available: 3
Project Location: Online and in person
Final assessment: Project presentation, 5-10 minutes
Contact: mailto:harini.desiraju@sydney.edu.au
MATH16: HEUN POLYNOMIALS AND HYPERBOLIC POLYGONS.
The Heun equation is a differential equation with deep connections to hyperbolic geometry. Any solution to the Heun equation gives rise to an angle preserving map from the upper half-plane to a hyperbolic polygon. In this project we will study the polygons corresponding to the simplest solutions of the Heun equation, the fascinating Heun polynomials.
Supervisor(s): Harini Desiraju, Pieter Roffelsen
Prerequisites: MATH2023, some experience with numerical plotting is desirable but not necessary
Maximum number of places available: 3
Project Location: Online and in person
Final assessment: Project report, 1-2 pages
Contact: mailto:harini.desiraju@sydney.edu.au
MATH17: Monodromy and cubic
surfaces.
Monodromy encodes how objects change as they move around singularities. When the objects in question are solutions of certain differential equations, this gives rise to beautiful and very classical surfaces known as cubic surfaces. It is a famous result in geometry that a cubic surface contains precisely 27 lines (counting multiplicity). In this project we study lines on these surfaces and what they can tell us about monodromy.
Supervisor(s): Pieter Roffelsen
Prerequisites: MATH2023: Analysis or MATH3061: Geometry and Topology
Maximum number of places available: 2
Project Location: The School of Mathematics & Statistics, Camperdown
Final assessment: Project report, 1-2 pages
Contact: mailto:pieter.roffelsen@sydney.edu.au