This session covers algebra, both as an abstract discipline in its own right, as well as the many interactions with fields such as geometry and topology. Topics range from universal algebra, group theory and ring theory through to homological algebra and K-theory.
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 applied statistics. Sessions held at previous AUST-MS meetings have featured talks covering a wide range of sub-disciplines including: bioengineering, bushfire modelling, cancer treatments, engineering mathematics, epidemiology, financial mathematics, game-theory, graph theory, granular materials, nanotechnology, numerical analysis, operations research, wave diffraction etc. Mathematically, this session encompasses a 'potpourri' of frameworks including deterministic and stochastic models.
Category theory is in the first instance a common language for the study of mathematical structures and their relationships, but is moreover the study of categories and their related notions as mathematical structures in their own right. Category theory began in the 1940s with the introduction of the basic notions of category, functor, and natural transformation by Eilenberg and Mac Lane in their study of certain relationships between topology and algebra, and the theory quickly developed in the following decades alongside its applications to such diverse fields as homological algebra, algebraic topology, algebraic geometry, universal algebra, logic, combinatorics, representation theory, and homotopy theory. Major areas of research in category theory include the study of categories with structure (e.g. monoidal categories and enriched categories), topos theory, categorical algebra, categorical logic, model categories, and higher category theory, to name but a few. In particular, the deep connection between higher category theory and homotopy theory is an important focus of current research. For this special session we welcome talks on category theory and its applications in all branches of 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 andnumerical 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.
Differential geometry is broadly defined as the study of geometric structures by analytical methods. This is one of the most well-represented areas in Pure Mathematics nationally. Special session in Differential Geometry will exhibit wide horizons of modern Differential Geometry in all its manifestations. The constellation of well-established researchers and younger speakers from Australia and overseas will present their most recent achievements in the broad range of interconnected topics, including parabolic, conformal, CR, complex, homogenous and Riemannian geometry.
Dynamical Systems and Ergodic Theory
This special session will feature recent advances in the areas of continuous and discrete time dynamical systems and ergodic theory. Talks will address developments in theoretical and applied lines of research by early and mid-career researchers as well as by established figures in the field.
Functional Analysis, Operator Algebras and Non-Commutative Geometry
Functional analysis is the study of topological vector spaces and operators between them. Common examples of such vector spaces are spaces of functions of various sorts. This theory has applications in many areas, for example to the study of partial differential equations.
Operator algebra is the meeting point of algebra and analysis, where the analytic techniques are employed to study the algebra of continuous linear operators on a topological vector space. It becomes a very effective tool in studying other fields of mathematics and physics such as dynamical systems, quantum statistical mechanics, and differential geometry. It also has outstanding applications in the areas of representation theory, graph theory, and number theory.
In noncommutative geometry, one models singular and otherwise intractable geometric and topological spaces by noncommutative operator algebras, generalising commutative algebras of functions on nonsingular spaces. Typical tools in this area are K-theory and its many generalisations, and a range of (co)homology theories. One area of applications is physics, where noncommutative geometry has implications to the standard model of particle physics, the fractional quantum Hall effect and string theory.
Geometric analysis, an extremely fertile research area lying in the intersection of differential geometry and analysis, involves probing into geometric and topological structures of manifolds by means of partial differential equations, with special focus on nonlinear PDEs arising in geometric and physical contexts. The behaviours of solutions of these PDEs serve to unveil deep information about manifolds, and have wide applicability in geometry, topology and physics. Conversely, problems from geometric analysis have motivated novel methods and techniques of studying geometric PDEs. Geometric analysis has been instrumental in the resolution of various important problems, such as the famous Poincaré conjecture.
In this special session we welcome talks in areas related to geometric analysis, including, but not limited to, general relativity, symplectic geometry, geometric flow, and gauge theory.
Geometry and Topology
Topology is the study of spaces, their properties, and continuous maps between spaces. This session will focus on topology and its applications, especially geometric topology and low-dimensional topology. Geometric topology is the study of manifolds and the maps between them, and low-dimensional topology focuses on manifolds and related spaces in dimensions two, three, and four. These areas have seen significant recent advances, and are well-represented in Australian mathematics. The session will also include topics on spaces and applications arising from geometry, where there may be additional metric properties. Applications of geometry and topology can be found in many areas of mathematics and other sciences, including algebra, combinatorics, and quantum physics to name a few.
Harmonic Analysis is one of the active research areas in modern mathematics, which has important roles in fundamental and applied mathematical research with extensive applications to other research fields such as partial differential equations, complex analysis, mathematical modelling and signal processing.
This special session on harmonic analysis will bring experts from oversea together with Australian experts as well as early career researchers and PhD. students. The talks to be presented will be the most recent significant developments and future directions of Harmonic Analysis and PDEs.
Integrable systems lies at the boundary of mathematics and physics and involves the study of systems whose solutions show a certain kind of regularity. The field comprises several well developed areas, such as classical integrable systems, soliton theory, exactly solvable models, quantum integrable systems, Painlevé equations and recent developments in birational geometry and discrete integrable systems. Although each of these areas has own problems, techniques and approaches, their interactions and interplay have always been prominently mathematical. This special session aims to gather Australian and international scientists working in various aspects of integrable systems, to encourage interaction and exchange of ideas.
Have you ever wondered how mathematics is used to model cell motility, heart disease, cancer treatment, epidemiology, evolution, and other phenomena? The field of mathematical biology keeps expanding, especially in Australia, with a growing number of research groups, PhD students, and postdocs. The breadth and novelty of problems continue to stretch our creativity to develop with more accurate mathematical models and more effective solutions. Real-world phenomena push us to devise ways to link a range of mathematical frameworks encompassing dynamical systems, agent-based models, continuum mechanics, graph theory, combinatorics, and group theory. This session will provide a survey of current research in mathematical biology throughout Australia.
The Mathematics Education special session focuses on tertiary mathematics education. Our session includes presentations of both theoretical research work and studies of innovative practices that colleagues have introduced in their classrooms.
The sessions are open to all, from the very experienced to the very new educators. We aim to build a supportive community where people can share their experiences and gain insight into new ways of thinking to help them improve their teaching and outcomes for students.
Topics include transition from secondary school, mathematics support, student retention, employability skills, online teaching and so much more!
We are also planning at least one targeted special session this year. If you have a burning issue that you would like to discuss, please contact me (Deb).
We hope to see you there!
The Mathematical Physics session provides a stage to present progress on the understanding of mathematical methods and structures that are used to address physically motivated problems. This includes but is not limited to equilibrium and non-equilibrium statistical physics, classical and quantum field theory, random matrix theory, general relativity, classical mechanics as well as quantum physics and quantum information theory. From a mathematical perspective the analysis of these systems typically involves combinatorial, representation theoretic or algorithmic aspects, the analysis of ODEs and PDEs as well as ideas from differential geometry and topology.
The number theory special session at the AustMS meeting is an excellent occasion for the Australian mathematical community to intersect with the growing pool of domestic number theorists. We expect talks covering analytic, algebraic, transcendental, and computational number theory. Some of these areas have intersection with combinatorics, cryptography, computing, and mathematical physics. In the past there has been a healthy mix of students, early career researchers and established academics. We anticipate this to continue in 2018.
While optimization has been widely utilized in solving many important problems from engineering, economy, biology, data science, to name just a few, it also enjoys fruitful interactions with many areas of mathematics such as functional analysis, variational analysis, combinatorics and computational mathematics. The special session, Optimization, will showcase the most recent mathematical and computational developments and their applications in continuous and discrete optimization, as well as in optimal control and calculus of variations. It aims to foster collaboration and promote further advances in the area, including the specialized topics, but not restricted to, variational analysis, optimal control theory, convex analysis, numerical optimization, polynomial optimization, nonsmooth optimization, vector optimization, stochastic optimization and functional analysis.
Probability Theory and Stochastic Processes
This is a broad session showcasing the breadth of current work in probability and stochastic processes that is ongoing in the Australian mathematical community. This includes but is not limited to: purely theoretical developments; mathematical and modelling aspects of applied work; and research relating to computational work.
Representation theory is the study of the basic symmetries of mathematics and physics. It is a very active field with many aspects at the center of recent advances in Geometry, Number Theory, and Theoretical Physics. The upcoming AustMS special session will report on recent progress, bringing together researchers from Australia and abroad working in representation theory, including but not limited to the topics of categorical structures, quiver varieties, geometric Langlands program, Springer theory, quantum groups, and modular representation theory.