Christopher Heyde Medal

Professor Serena Dipierro, University of Western Australia

After moving to Australia, first to the University of Melbourne and then to the University of Western Australia, Professor Serena Dipierro has significantly contributed to several fields in mathematical analysis, partial differential equations, nonlocal equations and free boundary problems. A characteristic treat in Professor Dipierro’s research consists in the fine analysis of the special patterns created by the interplay between nonlinear and nonlocal structures, also in light of motivations coming from biology and physics. Her works established the regularity properties and the geometric features of the interfaces arising from phase transitions, with special attention to the brand-new, and often very surprising, phenomena produced by far-away particle interactions and by the energy contributions ‘coming from infinity’. Her findings comprise the solution to challenging problems and the opening of brand-new lines of research, which will remain as a solid source of inspiration for future investigations on a number of emerging topics.

Dr Christopher Lustri, University of Sydney

It is often impossible to write down exact mathematical expressions to perfectly describe extremely complex natural systems such as the collective behaviour of a colony of ants, gravitational waves generated by orbiting black holes, or the flow of air over an aircraft’s wing. Asymptotic approximation theory can accurately predict how these complicated systems will change and evolve, even when they are far too complicated to solve exactly. Dr Christopher Lustri is an expert in developing new asymptotic approximation methods that capture important behaviour which is hidden from widely-used classical approximation techniques. Using these new methods, he has resolved open mathematical problems arising in practical scientific settings, such as explaining the shape of waves that form behind submerged obstacles, or the energy loss experienced by pulses in laboratory particle chains. He discovered that complex discrete systems contain important ‘tipping points’ that were previously unknown. If subtle changes are made to how the system is set up when the system is near one of these points, its behaviour can change dramatically. Dr Lustri’s methods make it possible to accurately capture how systems behave when they are near these tipping points.

Dr Valentina Wheeler, University of Wollongong

Dr Valentina Wheeler is a geometric analyst who has made major contributions to the field of elliptic and parabolic partial differential equations. In particular, her work focusses on geometric flows called curvature flows. These describe the movement and/or evolution of a curve or surface through space and time via continuous geometric deformation determined by curvature. Valentina’s contributions include resolutions of open conjectures regarding partition problems and existence of minimal hypersurfaces; completely novel types of singularities for curvature flows; the first global analysis of the Helfrich functional; and a powerful new Harnack convergence argument for fully nonlinear curvature flows with non-smooth speed. Her results include direct applications to real-world problems including modelling for the blood disease spherocytosis, behaviour of other biological membranes, and motion and evolution of merging fire fronts.

Dr Francis Hui, Australian National University

Dr Francis Hui’s research focuses on the development of innovative, fast approaches for the statistical analysis of big data, particularly when many correlated variables are collected in space and/or time to produce richly correlated data. He has made substantial contributions to the literature on efficient approximate methods for fitting multi-level models, techniques for data visualisation of many variables and scalable tools for flexibly fitting non-linear models and for selecting which predictors to include in complex correlated data settings. Dr Hui works at the interface between methodological and applied statistics, ensuring that his research has an immediate and substantial impact on the wider scientific community. His research has been particularly impactful in ecology, where his methods and software are applied by practitioners to project spatio-temporal change of species assemblages under climate change scenarios and for enhancing the understanding of terrestrial and marine ecosystems both across Australia and internationally.

Dr Kevin Coulembier, University of Sydney

Dr Coulembier’s research is in the field of mathematics known as representation theory, which studies how abstract algebraic structures are manifested as the solutions to concrete systems of linear equations. This field retains a strong connection to its origin as the study of geometric symmetry both discrete and continuous, but more recently has developed far beyond this in tackling curved and infinite-dimensional spaces and arbitrary number systems. One of Dr Coulembier’s most important discoveries was of a way to detect the presence of the classical type of symmetry known as an affine group scheme in a more exotic setting known as a tensor category; this problem had defied the efforts of some of the world’s top mathematicians for almost thirty years. He has also solved several other important problems in infinite-dimensional representation theory, and has discovered new unified proofs of major theorems concerning the invariants of groups and supergroups.

Dr Vera Roshchina, UNSW Sydney

Dr Roshchina is an exceptional mathematician and emerging international leader in the field of non-smooth optimization. Her main interest lies in finite dimensional geometry, more specifically, open problems that originate from continuous optimization and related fields. Some significant problems of this kind are in the geometry of polytopes, for example the polynomial Hirsch and Durer conjectures, critical point problems (Fekete problem, Sendov's conjecture) and convex variational problems, such as asymmetric Newton's aerodynamic problem. Resolution of these challenges is critical for making progress with numerous applications, from engineering and economics to medical research and data analytics.

Dr Jennifer Flegg, University of Melbourne

Drug resistance is a growing issue for malaria control. Dr Jennifer Flegg develops predictive statistical models in space and time for the level of drug resistance. These predictive models fill in the gaps where no information is available on drug resistance and have been used by health agencies to develop new polices about where and when certain drugs are appropriate to use.

Dr Flegg also develops mathematical models to describe and help understand the ways that cells and chemicals interact with each other during the healing of a skin wound. By building models that simulate the successful healing of a wound, she provides biological insight into the underlying healing mechanisms. In the case when a wound would not heal without intervention, she uses her models to predict how treatments can help the wound to heal.

Professor Ryan Loxton, Curtin University

Professor Ryan Loxton is pioneering new mathematical algorithms for optimising complex systems in a wide range of applications such as mining, robotics, agriculture, and industrial process control. Such systems are typically of enormous scale in practice, with hundreds of thousands of inter-related variables and constraints, multiple conflicting objectives, and numerous candidate solutions that can easily exceed the total number of atoms in the solar system, overwhelming even the fastest computers. Professor Loxton’s research provides new mathematical advances for overcoming this complexity and deriving fast algorithms for real-world use. He has collaborated with many companies with his work leading to innovative mathematical techniques for solving real-world problems such as providing algorithms for an award-winning Quantum technology platform that optimises the sequence and timing of maintenance activities in mine plant shutdowns.

Professor Geordie Williamson FAA FRS, University of Sydney

Professor Williamson is a world leader in the field of geometric representation theory. Among his many breakthrough contributions are his proof, together with Ben Elias, of Soergel's conjecture—resulting in a proof of the Kazhdan-Lusztig positivity conjecture from 1979; his entirely unexpected discovery of counter-examples to the Lusztig and James conjectures; and his new algebraic proof of the Jantzen conjectures.

Dr Zdravko Botev, University of New South Wales Sydney

Dr Zdravko Botev has developed innovative methodologies that aim to understand the probability structures underlying the occurrence of high-cost, hard-to-predict events. The novel rare-event simulation algorithms he has derived have not only advanced the fields of computational statistics and applied probability, but have been applied in multiple domains, including communication and computer network design, digital watermarking, safety assessment of debris collision in space and chemical geology. His well-cited research further demonstrates the significant influence of his work in his field of applied probability, as well as applications in many areas. His work has also had significant influence in the field of computational statistics, where his methods have been used in innovative ways to develop very fast algorithms for fitting flexible, smooth models to noisy data.

Dr Luke Bennetts, University of Adelaide

Dr Bennetts is an applied mathematician who models how waves of various kinds, e.g. acoustic waves, electromagnetic waves and waves at the surface of the ocean, are affected by solitary objects or assemblages of objects in their path. A major focus is on how ocean waves interact with ice floes in the polar seas, as this phenomenon appears to be a key contributor to the changes the Earth is experiencing in the Arctic Basin and the Southern Ocean due to the onset and furtherance of global climate warming. Because the polar regions are so important to the world’s atmosphere and oceans, the methodology that Dr Bennetts has created is also immediately applicable to the refinement of hemispheric-scale, coupled, operational climate forecasting, as well as contemporary research schema. His fusion of analytical technical mathematics with sophisticated computational methods allows real world problems, including nonlinear modes of behaviour, to be tackled and solved. 

Associate Professor Catherine Greenhill, University of New South Wales

Associate Professor Greenhill is internationally recognised as a leading expert in asymptotic, probablilistic and algorithmic combinatorics, undertaking research at the interface between combinatorics, probability and theoretical computer science. By studying fundamental combinatorial objects, such as graphs, she tackles problems of major significance to pure mathematics. Her highly-cited research achievements include new formulae and algorithms that have found broad application in many areas, from statistics to computer science, physics and cryptography.

Dr Scott Morrison, Australian National University

The interaction of quantum particles or quasi-particles in two dimensions involves a so-called “fusion category” which describes the possible outcomes of collision between the quasi-particles. Diagrams describing the fusion category are analogous to the Feynmann diagrams well known in quantum field theory. Dr Morrison has made remarkable discoveries especially in this diagrammatic description of such low-dimensional processes. In particular he has classified the least complicated such theories that mathematics permits.

Associate Professor David Warton, University of New South Wales

Associate Professor David Warton has made a series of highly significant contributions to data analysis in ecology - new methods for studying size variation, ecological communities and their climatic response, and the spatial distribution of species. Associate Professor Warton's contributions have had substantial influence on statistical practice across disciplines - used in a very large number of articles, in statistics, ecology, other areas of biology, the Earth sciences, agriculture, medicine, chemistry, psychology, engineering, and physics.

Dr Josef Dick, University of New South Wales

Dr Josef Dick is an outstanding young researcher who has undertaken pioneering research in the area of numerical analysis. His main research achievements relate to numerical integration and, in particular, quasi‐Monte Carlo rules. The importance of Dr Dick’s research derives from his ability to obtain practical constructions of well distributed point sets for use in applications from finance, statistics, physics, geoscience and other areas, as well as through rigorous mathematical convergence bounds using advanced mathematical tools.

Dr Anthony Henderson, The University of Sydney

Anthony Henderson has made fundamental contributions in representation theory, an area which concerns the algebraic patterns underlying collections of geometric transformations. He has invented geometric spaces which give new information about common symmetry types, and has introduced new methods for performing calculations in existing geometric spaces which take their symmetry into account. His work combines ideas from different areas of mathematics, and provides explicit formulas for use in a wide range of problems which involve observations on spaces with symmetry.