Mathematical Sciences Interdisciplinary Research Group
UNE has a proven record in supporting and producing high quality mathematical research, as evidenced by ERA (Excellence in Research for Australia) 2018 ratings of 5 (well above world standard) in Mathematical Sciences and Pure Mathematics. This research group, with particular research strength in partial differential equations and geometry, performs research across a broad range of theory and applications, covering topics of multidisciplinary nature using methods from mathematics, statistics and computational science. Our interests include:
- Agent based modelling
- Applied statistical modelling
- Collective behaviour
- Combinatorics
- Computational algorithms
- Cryptography
- CR-geometry
- C* algebras
- Dynamical systems
- Emergent pattern formation
- Modelling in biology, ecology and sports science
- Operations research
- Partial differential equations
- Real and complex differential geometry
- String theory and quantum field theory
- Topological Data Analysis
- Topology
See Publications from members in the Mathematical Sciences Interdisciplinary Research Group here. (ARC Australian Laureate Fellowship, 2024-2029, $2,450,000) Investigator: Prof. Y. Du This project aims to develop partial differential equation (PDE) theory and techniques to significantly improve the understanding of propagation and aggregation phenomena occurring in ecological invasion, disease spreading, krill swarming and elsewhere. To better capture real-world contexts, this research will establish new theories and techniques for PDEs over spatial domains that are not fixed, but change with time, and build models which are capable of significantly improving the human control and prediction of these phenomena. This project will generate a highly competitive team of Australian mathematicians with critical skills in a fast-progressing area of international interest. (ARC Discovery Project Grant, 2025-2027, $650,000) Investigators: Dr Johanna Knapp, Dr Jock McOrist This project aims to uncover new connections between mathematical structures by studying their physics in string theory. It will generate new knowledge in physics and pure mathematics using an interdisciplinary approach utilising a remarkable collection of symmetries, known as dualities. Expected outcomes from this synthesis of research fields include a new understanding of quantum corrections in both string theory and the mathematics of algebraic and differential geometry with cross-institutional collaborations at the national and international level. Significant benefits include bringing leading international researchers to Australia, cutting-edge research outcomes and research training in high profile international collaborations. This project is joint with University of Melbourne with partner institutions University of Oxford (UK) and University of Stavanger (Norway). Collaborators include Professor Philip Candelas FRS (Oxford), Professor Xenia de la Ossa (Oxford), A/Professor Eirik Svanes (Stavanger). (ARC Discovery Project Grant, 2024-2026, $390,000) Investigators: Dr Gabriele Tartaglino-Mazzucchelli, Dr Jock McOrist, Professor Peter Bouknewgt This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics. This project is joint with University of Queensland, Australian National University with partner institutions University of Chicago (USA) and University of Padova (Italy). Collaborators include Professor Savdeep Sethi (University of Chicago) and Professor Alessandro Sfondrini (Padova). Investigators: Prof. Gerd Schmalz and Dr Masoud Ganji This project is focused on a wide range of interrelated areas of Differential Geometry and Geometric Analysis. Cauchy-Riemann-geometry has its roots in the study of the geometric properties of boundaries of domains in complex space. In recent time it has received much attention in Differential and Riemannian geometry. On the one hand, Cauchy-Riemann manifolds serve as test objects for the general machinery of parabolic geometry, on the other hand, there is a deep relation between CR geometry and Riemannian, pseudo-Riemannian and conformal geometry, which was established by Fields prize winner (and 2016 Wolf prize winner) Charles Fefferman. Particular aims of the project are: studying mappings and embeddings of CR-manifolds into other CR-manifolds and complex space, exploring the relation between CR-manifolds and its generalisations with shear-free Lorentzian geometry, finding new classes of homogeneous CR-manifolds and classifying flat Sasakian manifolds. Investigators: N. Brownlowe, D. Robertson, C. Voigt, M. Whittaker Building upon our recent combinatorial characterization of the quantum automorphism group of a homogeneous rooted tree, G, via the rigid tensor category of tubular partitions, this project shifts focus to discrete quantum self-similarity. We investigate the construction of Quantum Iterated Monodromy Groups by lifting classical wreath recursion into the setting of infinitely iterated free wreath products. A primary objective of this project is to leverage these self-similar structures to isolate discrete quantum groups exhibiting intermediate growth—seeking a non-commutative counterpart to the foundational role that groups like the Grigorchuk group played in resolving the Milnor problem for classical groups. “Reflections on Compassionate Inquiry® and Teaching Mathematics” - Blog by Bea Bleile “Resolving Math-Anxiety Through Trauma-Informed Teaching” - Podcast by Bea Bleile “Mathematical Biology SIG of ANZIAM”Professor Yihong Du Professor in Mathematics ydu x3066 Professor Gerd Schmalz Professor in Mathematics schmalz x3182 Associate Professor Timothy Schaerf Associate Professor in Applied Mathematics tschaerf x5832 Dr Adam Harris Senior Lecturer aharris5 x2210 Dr Beatrice Bleile Senior Lecturer in Mathematics bbleile x3572 Dr Jock McOrist Senior Lecturer in Mathematic jmcorist x3142 Dr Brenda Vo Senior Lecturer in Statistics bvo3 x1896 Dr David Robertson Lecturer in Mathematics drober54 x1967 Dr Jelena Schmalz Lecturer in Mathematics jschmalz x2669 Dr Robert Cope Senior Lecturer in Statistics rcope4 x1547 Dr Masoud Ganji Lecturer in Mathematics (Teaching-Focus) mganjia2 x1192 Dr Wenjie Ni Lecturer in Mathematics wni2 x1088 Professor William Billingsley Professor in Computational Science wbilling x2513 Associate Professor Mitchell Welch Associate Professor in Computational Science mwelch8 x5004 Dr Peter Loxley Lecturer in Computational Science ploxley x2307 Associate Professor David Paul Associate Professor in Computational Science dpaul4 x2447 Dr Vera Miloslavskaya Lecturer in Information Technology vmilosla x4472 Dr Sophie Collins Lecturer in Statistics scolli40 x1930 Dr Zhoua Ma Postdoctoral Research Fellow in Mathematics “Partial differential equations for propagation and aggregation”
“The Physical Mathematics of String Dualities”
“Reaching new frontiers of quantum fields and gravity through deformations”
“Cauchy-Riemann Geometry”
“Discrete self-similar quantum groups”
Contact
Professor Yihong Du, Email: ydu@une.edu.au, x3066
