COMPUTER-ASSISTED RESEARCH MATHEMATICS AND ITS APPLICATIONS

Algebra

The Algebra session aims to present a diverse range of talks covering all algebraic interests represented in Australia. Talks on computational algebra or involving interactions with other fields are welcome. We particularly encourage students and early career researchers to take this opportunity to talk with others about their work.

Applied and Industrial Mathematics

The Applied and Industrial Mathematics session provides a 'catch-all' forum for talks across the fields of applied and industrial mathematics, including statistics. Sessions held at previous AUST-MS meetings have featured talks covering a wide range of sub-disciplines including: bioengineering, bushfire modelling, cancer treatments, climate, combustion, computing science, ecology, education, electrochemistry, engineering mathematics, epidemiology, financial mathematics, fluid mechanics, game-theory, graph theory, granular materials, Lie group methods to solve PDEs, logistics, nanotechnology, numerical analysis, operations research, synchronisation, travelling waves, wave diffraction etc.

Mathematically, this session encompasses a potpourri of frameworks including deterministic and stochastic models.

Computational Mathematics

Mathematical research in any areas of science where scientific computing plays a central role is included in computational mathematics. Computational mathematics involves designing and analysing algorithms and numerical methods to solve mathematical problems arising from science and engineering. One major area of computational mathematics is to solve equations (integral equations, ordinary differential equations, partial differential equations, fractional differential equations, stochastic differential equations, etc.) using approximation methods (finite element methods, finite volume methods, boundary element methods, meshless methods, kernel methods etc.) on computers.

Cryptography, Coding Theory and Related Topics

Cyber attacks are great threats in all aspects of life. Cybersecurity is the art of protecting digital networks, mobile devices, and data from unauthorized access or criminal use and the practice of ensuring confidentiality, integrity, and availability of information using cryptographic and coding techniques. When used appropriately with the right strategies, these techniques help to protect intellectual property from being susceptible to cyber threats and adversaries.

Modern cryptography uses various fields of mathematics such as number theory, field theory, coding theory, algebra, algebraic geometry, etc. The main mathematical principle in cryptography is that the mathematics that cryptographic schemes rely on should be based on the intractability of a mathematical problem (i.e., it should be very hard to solve by a brute force attack without knowing the secret key). In order to reduce cyber threats it is important to better understand the attacking behaviour of malicious objects in digital networks. Cryptology, the science of code breaking, deals with this question.

In this special session we will see the recent developments in modern cryptography and coding theory as well as the mathematical progress in cryptology.

Dynamical Systems and Ergodic Theory

We welcome talks across a broad range of topics in dynamical systems and ergodic theory including theory, numerics, and applications.

Equity, Diversity and Inclusivity in Mathematics

The Equity, Diversity and Inclusion special session invites contributions and participation from members of the community on issues relating to justice and equity in the mathematical sciences and society in general. Questions of interest may relate to issues of access, intersectionality, discrimination, belonging and identity, worldview and values, health including mental health, and the value of diversity as a positive thing for progress in mathematics. The format will allow for both individual presentations, as well as more collective fora. We aim to create a safe environment and opportunities for people to be heard.

Geometric and Harmonic Analysis

Many recent breakthroughs in harmonic analysis make crucial use of tools from incidence geometry, by which one exploits a deep connection of the problem at hand with curvature in the underlying geometry. In return, many problems in geometric analysis are deeply connected with estimates that are traditionally seen as part of harmonic analysis, with the role of Gagliardo-Nirenberg inequality in the Yamabe problem being a prominent example. This special session aims to bring together researchers in harmonic and geometric analysis, to discuss their recent work and explore possible synergies.

Geometry with Symmetries

The session will focus on modern trends in Differential Geometry and related areas, with an emphasis on group actions and symmetries.

Harmonic Analysis and Hyperbolic PDEs

Harmonic analysis lies in the frontier of modern mathematics. Over the past 60 years, Euclidean harmonic analysis has been inextricably linked with partial differentiable equations (PDEs). While applications to the theory of elliptic PDEs and pseudo-differentiable operators were a driving force in the development of the Calderón-Zygmund school from the very beginning, the past 20 years have also seen an influx of harmonic analysis techniques to the theory of nonlinear dispersive equations such as the Schrödinger and wave equations. These developments continue to this day. This special session will enable both international and Australian researchers to discuss their recent progresses in harmonic analysis, hyperbolic and dispersive partial differential equations.

Indigenising University Mathematics

The purpose of this session is to give a voice and support to those interested in finding ways to Indigenise Mathematics at University. What it means to do this is partly the topic of the session, as the concept is just beginning to be explored and may apply across a range of the aspects of our academic lives, including our teaching approaches, content, protocols of respect for Australia's First Nations Peoples and knowledge systems, as well as our underpinning values and philosophies.

The impetus for introducing the session at this time is a sense of a growing momentum in this space, especially around Indigenising Undergraduate Curriculum. The call to do this is coming at many levels, partly from individual connections and relationships between academics, Indigenous and non-Indigenous; and partly from institution-level requests to Schools, Departments and Disciplines.

Indigenising University Mathematics is challenging in interesting ways that may, in the long run, help us to understand ourselves and our own discipline better. In the short run, it is not necessarily easy to know how to start. The examples that are emerging in other disciplines are only partly helpful, since they are often in subject areas with more obvious connections to the Australian landscape or skyscape (like Food Science or Astronomy), so that connections to specific traditional knowledge may be more evident than in our space.

This session, hosted in partnership between an Anglo-Australian Mathematician and an Indigenous Education Academic, is based upon the predicate that meaningful Indigenisation is possible within Mathematics. This base-line assumption is built upon a combination of our personal experience starting to do this within various University Mathematics courses, and many interactions with other colleagues working towards the same goal.

We invite the Australian Maths Community to explore this space with us. If you are interested and want to share your thoughts, please make a submission for a talk. We expect submissions to very often have much more the character of a work-in-progress than might be expected in other sessions, because the endeavour is so new to many of us. We are interested in people's ideas, experiences, concerns, challenges, partial solutions and questions.

Integrable Systems and Mathematical Physics

Mathematical Physics lies at the boundary of mathematics and physics. The field comprises several well developed areas, such as classical integrable systems, exactly solvable models, quantum integrable systems, Topological Field theory, Conformal Field theory, Painlevé equations and recent developments in birational geometry and discrete dynamical systems. Whilst each of these areas have their own interesting problems, techniques and approaches, their interplay is also very rich and prominent. This special session aims to gather Australian and potentially international scientists working in various aspects of Mathematical Physics, to encourage interaction and exchanges of ideas.

Mathematics Education

This special session welcomes topical and engaging presentations on any aspect of mathematics education. This includes but isn't limited to current challenges in our context, including those relating to the aims of University Mathematics Education, academic integrity and assessment, digital learning and teaching, service teaching, and inventive ways of addressing these challenges.

Noncommutative Geometry and Operator Algebras

A special session to highlight recent Australian and New Zealand research in these fields.

Number Theory and Algebraic Geometry

We welcome talks on any topics in number theory and/or algebraic geometry. Given the breadth of these fields, talks on research that falls on interconnected topics in number theory, algebraic geometry and representation theory may also be considered. This session will provide a much needed platform to interact with fellow researchers and disseminate research findings.

Optimisation

Mathematical optimization is the study of using mathematics to make better decisions when faced with competing options. Both geometry and numerical considerations feature prominently. Applications are many; they include both aspects of design and operations. Talks in this session will be about the theoretical and computational aspects of optimization. Topics include variational analysis, optimal control, algorithms, mathematical programming, and error bounds.

Partial Differential Equations: From Theory to Applications

The main focus of this session are recent results of highest standard in research fields related to Analysis and Partial Differential Equations.

This session aims to bring together specialists in these fields.

Probability Theory and Stochastic Processes

This session will focus on recent advances in the research areas of probability theory and its numerous applications. This session aims to bring together specialists in these fields, including but not limited to the theory of stochastic processes, Monte Carlo methods, mathematical finance etc.

Representation Theory

Talks in this session will focus on representation theory understood broadly to include geometric and categorical representation theory as well as representation theoretic concepts emerging from physics. If interested, please submit a talk with an abstract.

Topology

This session is for topology across Australia, broadly interpreted. It includes low-dimensional topology, knot theory, geometric topology, algebraic topology, and interactions of topology with other fields.

Visualisation and Mathematical Art

Visualisations of mathematical ideas can be both instructive and attractive. In this session, speakers are invited to explain how a picture or physical object of their own original construction assists the viewer to visualise a mathematical concept and/or to describe aesthetic decisions they made as creator. This session will potentially traverse many areas of mathematics, and we invite a range of visualisations (e.g., digital, painting, sculpture, fibre arts).