Prof Kostya BOROVKOV 

Probability theory
limit theorems for random processes, large deviations, stochastic modelling

Financial mathematics
pricing of exotic options

Risk theory

Prof Jan DE GIER 

Mathematical Physics
integrable stochastic processes, exclusion processes, supersymmetric lattice models

Solvable Models/Combinatorics
integrability, discrete holomophicity, plane partitions

Dr Mark FACKRELL 

Stochastic Modelling
Queueing theory, Matrixanalytic methods

Operations Research
Game theory, stochastic optimisation, machine learning

Healthcare modelling
Patient flow in hospitals, donor flow in donor centres

Prof Peter FORRESTER 

Random Matrices
integrability properties, correlation functions, applications

Combinatorics and Statistical Mechanics
dynamical processes, RobinsonSchenstedKnuth correspondence, queues

Number Theory and Physics
Riemann zeta function, substitution sequences, quasicrystals and tilings

A/Prof Craig HODGSON 

Low dimensional topology
3manifolds, geometric structures, knot theory

Hyperbolic geometry
hyperbolic manifolds, polyhedra, computational methods

Differential geometry
geodesics, minimal surfaces, curvature flows

Prof Deborah KING 

Tertiary mathematics education: curriculum
assessment, feedback

Pedagogy
active learning, flipped classrooms, problembased learning, transfer

Students
transition, graduate attributes, students as partners

Prof Paul NORBURY 

Algebraic geometry
moduli space of Riemann surfaces, enumerative geometry, cohomological field theories

Gauge Theory
Higgs bundles, instantons, monopoles

Mathematical Physics
integrable systems, string theory, moduli space of super Riemann surfaces

Prof Aleks OWCZAREK 

Statistical Mechanics
Polymeric systems

Mathematical Physics/Integrable models
Exact solution of lattice models, critical phenomena

Computational physics/algorithms/simulation
Monte Carlo algorithms and simulations

Prof Paul PEARCE 

Exact solution of 2d lattice models
polymers, percolation, height, spin and vertex models

Statistical Mechanics
physical combinatorics, boundary properties, fractals

Connections with Conformal/Quantum Field Theory
finitesize corrections, scaling dimensions, fusion

Professor Gordon SMYTH 

Statistical bioinformatics
Empirical Bayes, overdispersion, multiple testing, RNAseq, ChIPseq, HiC, cancer genomics

Computational statistics
generalized linear models, REML, R programming

Prof Antoinette TORDESILLAS 

Data Analytics for Characterisation of Granular and other Heterogenous Media
Complex Networks, Machine Learning and Dynamical Systems

Modelling Complex Media and Systems
Structural Mechanics and Optimization of Networks

Generalized Continuum Theory and Modelling

Prof Aihua XIA 

Distributional approximations

Point Processes

Markov processes

Prof Sanming ZHOU 

Algebraic Graph Theory
arctransitive graphs, Cayley graphs, eigenvalues of graphs

Network Optimization
graph algorithms, colouring and labelling, routing and gossiping

Theoretical Computer Science
network design, perfect codes, isoperimetric problems for graphs, expansion of graphs

Emeritus Professor Anthony (Tony) GUTTMANN 

Enumerative combinatorics
generating functions, percolation

Lattice statistics
exact solutions, Ising models, selfavoiding walks

Algorithm design
transfer matrices, finite lattice method

Prof Peter TAYLOR 

Stochastic Models
Markov chains, matrixanalytic methods, stochastic fluid models

Queueing Systems
decay behaviour, multidimensional queueing systems, queues with advance reservations

Applications
telecommunications, mathematical biology, reliability

Prof Ian GORDON 

A/Prof Graham HEPWORTH 

Discrete interval estimation
confidence intervals for a binomial parameter

Group testing
estimation of proportions when units are pooled for testing

Associate Professor Lawrence REEVES 

Geometric group theory
curvature conditions, boundaries, decision problems

Low dimensional topology
polyhedral metrics, normal surfaces, coarse geometry

Professor Andrew ROBINSON 

Biosecurity
datamining, surveillance, risk analysis

Forest and Natural Resources Biometrics
modelling, inventory, monitoring

A/Prof Guoqi QIAN 

Statistical modelling and methods
generalised regression models, Markov chain Monte Carlo, model selection, time series analysis

Statistical machine learning
association rule mining, clustering and classification, information retrieval, stochastic sampling and search

Applied statistics
statistical climatology, statistical ecology, statistical genetics and genomics, statistical signal processing

Prof Aurore DELAIGLE 

Nonparametric Statistics
measurement errors, curve estimation, asymptotic theory.

Functional data

Analysis of fMRI data

A/Prof Sophie HAUTPHENNE 

Stochastic Processes
Markov chains, branching processes, queueing theory

Applied probability
Matrixanalytic methods, population biology and ecology, epidemic models

Statistical inference
Stochastic models

Prof Arun RAM 

Representation theory
lie type groups, quantum groups, lie algebras

Algebra, geometry, topology
centralizer algebras, reflection and braid groups, flag varieties

Algebraic Combinatorics
symmetric functions, young tableaux, walks in buildings

Dr Stephen MUIRHEAD 

Probability theory
Random fields, Gaussian processes, percolation, random walks in random media

Professor Paul ZINNJUSTIN 

Mathematical Physics
exactly solved models

Algebraic Combinatorics
symmetric functions, Schubert calculus

A/Prof Nora GANTER 

Representation theory
homotopy theory, generalized characters

Categorification
characters of 2representations, poweroperations

Moonshine
Hecke actions, equivariant elliptic cohomology

A/Prof Alex GHITZA 

Number theory
modular forms, elliptic curves, Galois representations

Computational Algebra
computational aspects of number theory, algebraic geometry

Representation theory
Langlands program, automorphic forms

Dr Davis MCCARTHY 

Genomic Data Science
Statistical and machine learning methods for the analysis of complex, highdimensional genomic data, particularly singlecell gene expression and other singlecell 'omics data

Bioinformatics
Development of statistical and machine learning methods and software for the analysis of singlecell 'omics data

Applied statistics
Bayesian data analysis, factor analysis, computational statistics, count data models, machine learning

Dr Lele (Joyce) ZHANG 

Operations Research
Scheduling

Statistical Mechanics and Stochastic Processes
Cellular automata

Applied Mathematical Methods
Traffic modelling

A/Prof David RIDOUT 

Mathematical Physics
conformal field theory, string theory, statistical mechanics

Representation theory
vertex algebras, KacMoody algebras, Lie algebras, Lie groups, cellular algebras

Algebra
tensor categories, modular forms, Verlinde formula

Dr Peter MCNAMARA 

Representation theory
Lie theory, quantum groups, padic groups, perverse sheaves (geometric representation theory)

Algebra
Categorification, highest weight categories

Dr Jesse COLLIS 

Micro & Nano scale hydrodynamics
Characterisation of nanoparticles, fluidstructure interactions, oscillatory viscoelastic flows

Acoustofluidics
Manipulation of nanoparticles, steady streaming flows, autonomous propulsion

Prof Kari VILONEN 

Representation theory
Real groups, the Langlands program

Algebraic geometry
Hodge theory, geometric Langlands program, microlocal analysis

Dr Mario KIEBURG 

Random Matrix Theory
integrability properties, correlation functions, applications (telecommunications, time series analysis, quantum field theory, quantum chaos, quantum information)

Supersymmetry & Graded Algebras
nonlinear sigma models, superbosonisation

Harmonic Analysis and Group & Representation Theory
Matrix Groups, Lie Algebras, Symmetric Spaces

A/Prof Nathan ROSS 

Probability theory
limit theorems, convergence rates, Stein's method

Stochastic Processes
Urn models, random networks and trees

Prof Howard BONDELL 

Computational statistics
Bayesian inference, regularisation, variational Bayes

Statistical Learning
Model selection, highdimensional data, robust statistical methods

Modelling and Analysis of Complex Data
Personalised medicine, missing data, hierarchical models

A/Prof Alysson COSTA 

Operations Research
Optimisation, Applied Discrete Mathematics, Mixed Integer Programming, (Meta)heuristics.

Prof Christian HAESEMEYER 

Algebraic geometry
Ktheory and trace methods, motives and motivic cohomology

Algebraic topology
Algebraic Ktheory of spaces, motivic homotopy theory

Algebraic Ktheory
Ktheory and trace methods, motives and motivic cohomology

A/Prof Marcy ROBERTSON 

Abstract Homotopy Theory
model categories, infinitycategories, higher category theory

Operads
weak algebras, GrothendieckTeichmueller group

Algebraic topology
algebraic invariants of spaces

A/Prof Charl RAS 

Algorithms
computational complexity, approximation algorithms, heuristics

Network design
Steiner trees, proximity graphs, network applications

Combinatorial optimisation
graph theory, integer programming

A/Prof Ting XUE 

Representation theory

Algebraic groups
Nilpotent orbits, Springer theory, Perverse sheaves

A/Prof James OSBORNE 

Multicellular Systems Biology
Cell Based Modelling of Development and Disease, Data fitting, Multiscale Simulations

Numerical Analysis and Scientific Computing
Finite Element Methods, Software Development, Multiphase Flow.

Mathematical Biology
Organ and Tissue Development, Cancer, Tissue Engineering, Biofilms

Dr Binzhou XIA 

Algebraic Graph Theory
arctransitive graphs, Cayley graphs

Group Theory
permutation groups, group factorizations

Dr Daniel MURFET 

Algebraic geometry
derived categories, singularity theory, geometric aspects of topological quantum field theory

Theoretical Computer Science
linear logic, categorical logic, theory of deep learning

Dr Heejung SHIM 

Genomic Data Science
Statistical and machine learning methods for the analysis of complex and largescale genomic data with applications to functional genomics. Bioinformatics, Omics data analysis, Genomewide association analysis of complex traits.

Applied Statistics and Machine learning
Bayesian data analysis, Computational statistics, Machine learning, deep learning.

Phylogenetics
Stochastic processes for modeling trait evolution on phylogeny, Phylogeny reconstruction from unaligned multiple sequences.

Prof James MCCAW 

Mathematical Biology
infectious disease epidemiology, immunology, virology, parasitology

Model selection and model fitting
deterministic and stochastic models, forecasting, Markov chain Monte Carlo

Prof Stephen LESLIE 

Statistical and population genetics
Detecting and controlling for population structure; demographic inference; association studies; imputation of complex genetic variation

Bioinformatics
Methods for single cell omics analyses; assembly of longread data

Dr Wei HUANG 

Nonparametric Statistics
Regression, Asymptotic theories

Functional data

Incomplete data
Missing scalar data or incomplete functional data analysis

Dr Thomas QUELLA 

Mathematical Physics
Conformal field theory, string theory, supersymmetry, quantum integrable models, theoretical aspects of machine learning

Strongly correlated quantum systems
Topological states of matter, quantum computing, tensor network states, quantum information theory, path integral methods

Representation Theory and Applications
Finite and infinite dimensional Lie (super)algebras, diagram algebras, quantum groups

A/Prof Diarmuid CROWLEY 

Differential topology
Surgery theory, exotic spheres, contact topology, 5678manifolds

Algebraic topology
Homotopy theory, bordism theory

Dr Jesse GELLREDMAN 

Partial Differential Equations
microlocal analysis, scattering and spectral theory

Differential geometry
index theory, analysis of singular spaces

Professor Mark HOLMES 

Probability and stochastic processes
Reinforcement processes, interacting particle systems, random walks, random media, Markov chains

Professor KimAnh LECAO 

Computational statistics
Dimension reduction, matrix factorisation, penalised regression

Big biological data
Analysis of single cell transcriptomics, microbiome, omics

Systems Biology
Data integration, Projection to Latent Structure models, Canonical Correlation Analysis

Dr Douglas BRUMLEY 

Fluid Dynamics
Swimming organisms, coral reef flows, transport processes

Biophysics
Cellular locomotion and navigation, chemotaxis, collective dynamics, synchronization

Dr Tingjin CHU 

Spatial statistics
asymptotic theory, spatial binary and count data, statistical climatology, spatial machine learning.

Statistical methodology
statistical computing for large data, model selection, traffic analysis

Dr Liuhua PENG 

Statistical inference for big data
distributed statistical inference, massive data

Extreme value theory with application in statistics and economics
Extreme value theory

Highdimensional data analysis
Highdimensional hypothesis testing, model selection

Professor Jennifer FLEGG 

Mathematical Biology
wound healing, tumour growth, infectious diseases

Applied statistics
computational Bayesian statistics, geospatial statistical mapping

Dr JeanEmile BOURGINE 

Mathematical Physics
String theory, Supersymmetric gauge theories, integrable systems, quantum groups, symmetric functions

Dr Stuart JOHNSTON 

Mathematical Biology
bionano interactions, collective cell behaviour, synthetic biology, animal navigation

Stochastic Modelling
random walks, extinction processes, continuum approximations

Dr Yaping YANG 

Representation theory
Lie theory, quantum groups, KnizhnikZamolodchikov equations, Cohomological Hall algebras

Geometry & Topology
Toric CalabiYau manifolds, oriented cohomology theory, quiver varieties

Prof Kate SMITHMILES 

Operations Research
combinatorial optimisation, multiobjective optimisation, modelling realworld problems, heuristic methods

Machine Learning
dimension reduction, classification, forecasting, clustering

Algorithmic Science
methodologies for performance analysis, generation of benchmark test instances

Dr Susan WEI 

Machine Learning
Reinforcement learning, classification and clustering

Applied statistics for biomedical applications
Personalised medicine, mobile health, medical imaging analysis

Statistical inference
Highdimensional hypothesis testing, changeplane models, dynamical systems

Dr Hailong GUO 

Numerical Solution of partial differential equations
Nonstandard finite element method, adaptive algorithms

Simulation of topological materials
Photonic graphene, Maxwellâ€™s equation, fast methods

Surface modeling and Computation
Manifold learning

Dr Chenyan WU 

Algebraic number theory
automorphic representations, theta correspondence, Langlands program

Algebraic geometry
Abelian varieties

Dr Gufang ZHAO 

Representation theory
Quantum algebras, homogeneous spaces, geometric and topological methods

Algebraic geometry
Symmetries, geometry motivated by physics, symplectic and hyperkahler spaces, singularities

Topology
Elliptic cohomology, motivic homotopy, applications in representation theory

Dr Pavel KRUPSKIY 

Modeling financial data
Volatility clustering, risk measures, joint distribution of asset returns

Spatial data and environmental applications
Covariance functions, spatial covariates, spatial interpolation

Modeling extremes
Tail probabilities, measures of dependence, tail dependence, heavy tails

Dr Volker SCHLUE 

Geometric analysis
analysis of PDEs, Riemannian and Lorentzian geometry, geometric flows

Partial Differential Equations
wave equations, hyperbolic partial differential equations in mathematical physics, continuum mechanics

General relativity
black holes, gravitational waves, cosmology, stars

Dr Mingming GONG 

Machine Learning
Causal Inference, Transfer Learning, Deep Generative Models

Computer Vision
3D vision, Face Recognition, Image/Video Generation

Biomedical Informatics
Gene Regulatory Network Learning, Medical Image Analysis

Dr Dennis LEUNG 

Highdimensional statistics
HighDimensional Asymptotics, Measures of Independence

Graphical models
Identifiability, Causal Inference

Multiple testing
False Discovery Rate, Adaptive Testing

Dr Johanna KNAPP 

Mathematical Physics
String theory, Supersymmetric field theories, Mathematics related to string theory (algebraic geometry, categories,....)

Dr Matthew TAM 

Continuous optimisation
iterative algorithms, monotone operator splitting, nonsmooth optimisation

Nonsmooth optimisation
setvalued and variational analysis, regularity notions, symbolic convex analysis

Applications of optimisation
imaging, signal processing, machine learning, heuristic derived from continuous optimisation

A/Prof Jack HALL 

Algebraic geometry
moduli spaces, algebraic stacks, derived categories, algebraization

Dr Christopher BAKER 

Mathematical Biology
Ecological modelling, Invasive species management, Infectious disease epidemiology

Applied statistics
Bayesian inference, model selection, intractable likelihood problems

A/Prof Agus SALIM 

Statistical bioinformatics
Generalized linear models for omics data, RNAseq, singlecell RNAseq data analysis

Risk Prediction Models
Genomics risk prediction, Lipidomics risk prediction with emphasis on cardiovascular disease

Statistical Models for realtime Data from Wearable Devices
Continuous Glucose Monitoring (CGM), Physical Activity Monitoring

Dr Camelia WALKER 

Mathematical Biology
Infectious disease epidemiology

Stochastic Modelling
Markov chains, models with population structure

Applied statistics
Bayesian inference, model selection, intractable likelihood problems

Dr Edward HINTON 

Environmental Fluid Dynamics
Modelling of CO2 storage, lava flows, ice sheets

Methods of Applied Mathematics
Asymptotic analysis, free boundary problems, similarity solutions of first and second kind

Dr Christopher DUFFY 

Graph Theory
Graph colouring and homomorphism, orientation problems, discretetime processes, dominating sets

Theoretical Computer Science
Graph algorithms and computational complexity
