# Current Research Students

Principal trace function of Carey-Pincus in semifinite setting and its connections with spectral shift functions

Banach algebras

Graph Theory and Hypergraphs

New applications of nonlinear analysis to nonlinear differential equations

Dynamical Systems and Optimization

Wavelets, non-parametric statistics, functional data analysis

Random Structures in Combinatorics

Quantifying Global Water Cycle Change using Ocean Observations

Universal Hyperbolic Geometry, Mobius Geometry and the Special Theory of Relativity

Improving the representation of the ocean surface mixed layer in an operational ocean forecast model

Computational Statistics and Data Science

Markov Chain Monte Carlo/Approximate Bayesian computation

Uncertainty Quantification for PDEs with random coefficients using Quasi-Monte Carlo Methods

New directions for the spectral method of transfer operators

Functional analysis

Mathematical oceanography, in particular identifying Langrarian Coherent Structures in the ocean using multi-drifter trajectory data

Cox process regression models for multi-species presence-only data in ecology

A posteriori error estimates of a convergent numerical scheme for a hyperbolic nonlinear problem

Anomalous diffusion models of limit order books

Mathematical modelling of the insulin signalling pathway in adipocytes

Population-level harms, benefits and cost-effectiveness of HIV vaccination strategies in developing countries

Chromogeometry and cubics over finite fields

Functional analysis, double operator integrals

Weak Type (1,1) Boundedness of Free Hilbert Transforms

Bayesian inference and Markov Chain Monte Carlo simulation

Regression to the mean effects in interrupted time series designs

Statistical Methods for Climate Model Ensembles

Self-exciting process, Point process, limit theory, asymptotic inference, financial data analysis, point pattern analysis

Deriving new ways of constructing approximately neutral surfaces

Geometric Fourier transform theory for compact simple Lie group connecting the Kirillov theory for representations with the operator valued Fourier transform

Stochastic Processes and Their Simulations

Elliptic orders

Regularisation methods in stochastic process inference

Analytic Number Theory

Extremal set theory

Functional Analysis

Non-Markovian random walks with applications to epidemiological models

Model-Based Assessment of Treatment Effect in Multivariate Abundance Data

Spectral shift function in Scattering Theory

Statistical Methods in Australian Rules Football

Modelling spatially correlated measurement error via Monte Carlo expectation maximization algorithm

The geometry of the tetrahedron and higher dimensional rational trigonometry

Higher order symmetries of Lorentzian manifolds

Construction Algorithms for Golomb Rulers

Geometric properties of finite dimensional Banach spaces

Biogeochemical modelling of the Tasman Sea

Discovering the Hidden Influence of Coherent Structures in Complex Geophysical Flows

Geometry of Banach spaces and noncommutative geometry

Point process, financial data analysis, time series, computational statistics

Integration theory for sigma operators

Point processes, statistical inference, applied statistics and probability, market research, stochastic modelling

Application of Bayesian statistics to inverse problems and high dimensional computation in finance

Functional analysis and partial differential equations

Observational Oceanography of Southeastern Australia

Symbolic data analysis

Stochastic processes and its relevant applications; Pricing and hedging of financial derivatives; Bayesian Statistics

Number Theory

Application of Fuzzy Set Mont Carlo Simulation - Estimating the Shortage of Bank's Branch Position

Yield Curve Estimation Methodology by Using Equilibrium Models

Partition Process in Data Analysis and Machine Learning

Random substitution of fractals on graphs and proof of the minimum clues in Sudoku

Stochastic process models for financial data analysis and their statistical inferences

A Generalised Principal Component Analysis Approach for Ecological Monitoring

Natural language analysis of poison information centre free text data

Generalisations and applications of the accumulating remainder tree

Generalised Inversion Count and Distribution of Integer Sequences