Joint Meeting of the NZMS, AustMS and AMS

9-13 December 2024

University of Auckland, New Zealand

Special Sessions-Descriptions


  • Harmonic analysis and Hamiltonian PDE
    Monica Visan, UCLA,, USA; Zihua Guo, Monash University, AUS; Rowan Killip, UCLA, USA
    Brief Description
    : This special session will focus on developments at the interface of harmonic analysis and dispersive PDE. Topics of active interest include: recent progress on completely integrable models, the role of decoupling in dispersive PDE, and new directions in harmonic analysis spawn by the introduction of external fields.
  • Computability Theory an Applications
    Rod Downey, Victoria University of Wellington, NZ,; Linda Westrick, Pennsylvania State University, USA
    Brief Description:
    Computability theory has seen significant progress in recent years, particularly in applications in Reverse Mathematics, Computable Analysis, and Algorithmic Randomness. For example, computable dimension has been applied to give new results in geometric messure theory via the “point to set” principle of Lutz and Lutz, such as the new extension to Marstrand’s projection formula. There have been interactions of computability theory with classical analysis, with proofs that computability hierarchies align with the classical Bourgain classification of Baire 1 functions, and techniques such as the true stage construction being used in descriptive set theory.
      This special session will bring together workers in these areas for hopefully fruitful interactions.
  • Mathematics Education
    Organisers: Tanya Evans, University of Auckland, NZ,; Deborah King, University of Melbourne, AUS; Edgar Fuller, Florida International University, USA
    Brief Description:
    The recent worldwide shift to online teaching as an emergency response to the COVID-19 pandemic has resulted in an unprecedented use of technology in educa1on at scale. It appears that a large majority of tertiary teachers have had to change the way they teach and embrace technology, putting their hesitation and trepidation aside. With the abundance of newly developed online resources and novel ways of delivery, the post-COVID-19 educational landscape is set to change rapidly, skipping a natural gradual stage of continuous developmental changes to the sector. This development could be a welcome breakthrough, but, as never before, it amplifies the big issue: research is lagging the implemention.
      With a stark sense of urgency, this special session will bring tertiary mathema1cs teachers and researchers from around the world to engage in sharing the latest research findings and showcasing successful practical implementa1ons. There are many pressing questions in terms of the future of mathematics lectures and the various forms of learning environments that could be designed to promote active learning.
  • Topology, geometry and combinatorics of biopolymers
    Nicholas Beaton, University of Melbourne, AUS,; Chris Soteros, University of Saskatchewan, Canada; Koya Shimokawa, Ochanomizu University, Japan; Mariel Vazquez, UC Davis, USA.
    Brief Description:
    The session will offer an opportunity to explore various hot topics in the study of biopolymers, with an emphasis on the guiding biological questions and on the mathematical, statistical and computational techniques that underlie their analysis. Of particular interest are the entanglement and 3-dimensional (3D) organization of biopolymers, the action of enzymes that change the topology and/or geometry of DNA and the entanglement of DNA-RNA hybrids. The ultimate goal is to strengthen the research and educational bridges within this interdisciplinary field in which mathematical and physical scientists interact with biologists, and to strengthen connections across the Pacific Rim region.
  • Deterministic and Probabilistic Aspects of Dispersive Partial Differential Equations
    Timothy Candy, University of Otago, NZ; Yu Deng, University of Southern California, Yu Deng,; Bobby Wilson, University of Washington; Xueying Yu, Oregon State University.
    Brief Description:
    This special session focuses on the recent exciting developments in the field of nonlinear dispersive equations. The central theme is to understand the long time behavior of these equations, from both deterministic and probabilistic aspects. Specifically, in this special session we will discuss topics including soliton resolution, formation of singularity, propagation of randomness and wave turbulence.
  • Differential geometry and geometric analysis
    Claude LeBrun, Stony Brook University, USA; Matt Gursky, University of Notre Dame, USA; Mike Eastwood, University of Adelaide, AUS; Rod Gover, University of Auckland, NZ,
    Brief Description:
    Differential geometry and geometric analysis have had a central role in mathematics and physics for well over 100 years. These areas are also much studied in Australia, the US, and New Zealand. Our proposal is to bring together expertise from different aspects of these areas with the hope stimulating new, as well as existing, collaborative work.

      The scope will range from the more algebraic representation theoretic aspects to the geometric analysis of curvature conditions. Ideas might be, for example, applied to the study of Einstein metrics, the existence of, or obstructions to, special geometric structures, prescribed curvature problems including for submanifolds, and eigenvalues of the Laplacian. Some particular interests are conformal techniques, curvature flow, holonomy, and special geometries – for example for example Hermitian, hyperKaehler, and G2 geometry.

  • Recent advances in geometric PDE
    Florian Beyer, University of Otago, NZ,; Joerg Frauendiener, University of Otago, NZ; Shoo Seto, California State University, Fullerton, USA; Bogdan D. Suceavă, California State University, Fullerton,USA; Mihaela B. Vajiac, Chapman University,USA.
    Brief Description:
    The present session aims to bring together a range of directions whose common theme is the use of geometric partial differential equations as broadly defined as possible. Examples are applications of partial differential equations to various geometric objects, including, but not limited to, the study of Riemannian, Lorentzian, Kaehlerian, symplectic and contact structures. In the last decades, various techniques produced new results, some of them inspired by the extensive study of Ricci and other flows, the Einstein’s equations in general relativity, geometric fluid problems etc.

      The proposed special session will also be interested in consequences for minimal submanifolds and their connection with various geometric functionals, submanifolds, complex and totally real submanifolds, as well as the study of Riemannian submersions with various classes of fibers. The proposed topic includes the study of curvature functionals in various contexts, comparison geometry, new curvature invariants, relations between curvature and topology, and other related topics.
      We also welcome discussions of numerical solutions of geometric partial differential equations.
    Our Special Session will welcome contributions of scholars in the earlier stages of their career development, including doctoral candidates and postdoctoral researchers whose academic interests lie in the realm of geometric partial differential equations.

  • 50 years of Communications in Algebra

    Organisers: Scott Chapman, Sam Houston State University, Huntsville, Texas,USA,; James East, Western Sydney University, Sydney, AUS.
    Brief Description: Communications in Algebra turns 50 years old in 2024. The journal was founded in 1974 by Earl Taft at Rutgers University with humble beginnings (at first papers were published from the author’s camera ready copy). It has now grown into one of the world’s largest algebra only journals, publishing over 5,000 pages annually. While publishing over the entire spectrum of algebra, the journal has established strengths in Commutative Algebra, Associative and Non-Associative Rings and Algebras, Representation Theory, Groups, and Semigroups.
      The purpose of our session is to not only look backwards and celebrate Communication in Algebra’s past, but also to look to its future and the vast amount of research being inspired by its recent articles. 
    We propose to have 2 Keynote addresses (one in Commutative and Non-Commutative Algebra with the other in Groups and Semigroups) to consider the impact of multiple past highly cited papers. According to Google Scholar, several of these papers have been cited more than 500 times. The Keynote addresses will be delivered by current or past Associate Editors.
      Communications in Algebra has played an important role in the direction of current research in the core areas outlined above, and our remaining talks will focus on recent work in these areas. These talks will be delivered by a variety of international speakers as outlined in the potential speakers list below. The session will have extremely broad appeal and will potentially draw participants from all areas of algebra and related fields.

  • Arithmetic Geometry and Number Theory
    John Voight, Dartmouth College, USA and University of Sydney, AUS,; Kiran S. Kedlaya, University of California, San Diego, USA; Brendan Creutz University of Canterbury, NZ.
    Brief Description:
    This session will be devoted to arithmetic geometry and number theory, with an emphasis on explicit methods. Specific mathematical themes include rational points on curves and surfaces, Galois representations, L-functions, analytic methods, cohomological invariants of varieties, the geometry of modular varieties, Diophantine geometry, and varieties over finite fields. We aim to bring together diverse researchers working in these areas in the hopes of fostering fruitful discussion and future research connections.
  • Computational Number Theory and Applications
    Steven Galbraith, University of Auckland, NZ; David Harvey, University of New South Wales, Sydney, AUS; Andrew Sutherland, MIT, USA.
    Brief Description:
    This session will be devoted to computational number theory and its applications, including algorithmic aspects of number theory and related fields. Topics for the session will be drawn from elementary number theory, algebraic number theory, analytic number theory, the geometry of numbers, arithmetic geometry, finite fields, Galois theory, cryptography, and coding theory.
  • Ergodic Theory and Dynamical Systems
    Boris Hasselblatt, Tufts University, USA,; Andy Hammerlindl, Monash University, AUS; Keith Burns, Northwestern University, USA.
    Brief Description:
    Subjects may include ergodic theory (combinatorial, abstract, smooth), hyperbolicity (uniform, nonuniform, partial), Hamiltonian and complex dynamics, bifurcation and stability theory, computational aspects, as well as applications to other fields of mathematics, to the sciences, and to machine learning.

  • Functional Analysis and Operator Algebras
    Astrid an Heuf Victoria University of Wellington, NZ,; Priyanga Ganasan, University of California San Diego, USA; Aidan Sims, University of Wollongong, AUS.
    Brief Description:
    The special session in Functional Analysis and Operator Algebras will feature talks in the general areas of functional analysis and operator algebras, both interpreted fairly inclusively. The scope of the special session covers a range of topics including: aspects of Banach-space theory and function spaces; algebras of operators such as C*-algebras and von Neumann algebras and related Banach algebras; operator-algebraic representations of algebraic, combinatorial and geometric objects; noncommutative geometry; and connections between these areas and other areas of mathematics.

      The session will feature a mixture of 20-minute and 50-minute talks, delivered by speakers including senior researchers, early-career researchers, and research students.

  • Probability and Mathematical Statistics
    Han Gan, University of Waikato, NZ,; and Jesse Goodman, University of Auckland, NZ,; Committee members Krzysztof Burdzy (University of Washington, USA), Andrea Collevecchio (Monash University, AUS), Simon Harris (University of Auckland, NZ), Thomas Taimre (University of Queensland, AUS), Ilze Ziedins (University of Auckland, NZ).
    Brief Description:
    The Probability and Mathematical Statistics session will include a mix of invited and contributed talks. Talks will be broadly grouped by themes, including: stochastic processes, branching structures, limit theorems and asymptotics, stochastic analysis, applied probability, and mathematical statistics.
  • Early Career Showcase in Low-Dimensional Topology
    Dave Auckly, Kansas State University,USA ,; Shelly Harvey, Rice University, USA; Josh Howie, Monash University, AUS; Arunima Ray, Max Plank Institute, Germany.
    Brief Description:

    This session will showcase the work of early career researchers in low-dimensional topology. Several senior researchers will attend the session to provide feedback to presenters and participants. In addition to longer talks featuring the work of the invited speakers, the session will include periods for lightning talks. These lightning talks will be open to anyone.

      Topology is now a large, well-developed field of mathematics. Even low dimensional spans a broad range of research topics. This session may include talks related to computational topology and quantum 3-manifold invariants. It may include more geometric topics such as hyperbolic knots, Dehn surgery, and complex projective structures. There is a bridge from knot theory to concordance, and from there to knotted surfaces and families of smooth structures. Here some symplectic topology may even make an appearance.

  • Index Theory in Geometry and Mathematical Physics
    Xianzhe Dai, University of California, Santa Barbara, USA,; Fei Han, National University of Singapore; Pedram Hekmati, University of Auckland, NZ; Varghese Mathai, University of Adelaide, AUS.
    Brief Description:
    The Atiyah-Singer index theory continues to find remarkable and significant applications, especially in geometry and mathematical physics. The purpose of this special session is to bring together experts and young researchers working in this direction and related fields, to exchange ideas and foster interactions.
  • Singularities
    Laurentiu Maxim, University of Wisconsin-Madison,; Laurentiu Paunescu, University of Sydney, AUS.
    Brief Description:
    The Special Session “Singularities” will bring together researchers interested in the study of the many facets of singularities, by using methods from algebraic and geometric topology, algebraic geometry, and geometric analysis. The Session will be research-oriented, intended to disseminate recent developments and strengthen connections among the various research groups represented.

      Singularity theory is a meeting place of many disparate areas of mathematics, where different types of ideas, techniques and results merge together. The modern theory of singularities dates back to the 1960s, with the pioneering work of Thom, Hironaka, Brieskorn, Zariski, Milnor, Arnold and many other celebrated mathematicians. More recently, Singularity Theory promoted vigorous interchanges among mathematical fields such as algebraic and geometric topology, algebraic geometry, number theory, and more applied fields such as computer vision, engineering, and the study of large data sets.
      The proposed Special Session will focus on the following topics, each driven by recent and fundamental advances: singularities of hypersurfaces, characteristic classes of singular varieties, applications of singularities in algebraic statistics, hodge theory, Lipschitz geometry.

  • Representation Theory and Tensor Categories
    Alexander Sherman, University of Sydney, AUS,; Nate Harman, University of Georgia, USA.
    Brief Description:
    This session will field talks on representation theory and tensor categories, broadly interpreted. Representation theory includes representations of natural algebraic objects such as Lie (super)algebras, (super)groups, quantum groups, and diagram algebras. The categories of representations in such cases form tensor categories, allowing the input of categorical techniques. More abstract tensor categories are of interest in their own right, and often lead to unifying ideas in representation theory.
      We aim to represent a large spectrum of topics in these fields, and encourage talks that are accessible to the non-specialist.
  • Mathematical Physics
    David Ridout, University of Melbourne, AUS,; Pedram Hekmati, University of Auckland, NZ, Justine Fasquel, University of Melbourne, AUS; Shashank Kanade, University of Denver, USA.
    Brief Description:
    The purpose of this special session is to bring together mathematical physicists in the broadest sense. We interpret this as the study of mathematical aspects of modern theoretical physics. The latter includes, but is not limited to:
      classical/quantum integrability
      condensed matter physics
      general relativity
      quantum computing/information
      quantum field theory (including conformal field theory, string theory and quantum gravity)
      random matrix theory
      statistical physics.
      We also welcome pure mathematicians working on mathematical structures inspired by these areas.
  • Special Functions, q-Series and Beyond
    Howard S. Cohl, Applied and Computational Mathematics Division, National Institute of Standards and Technology, USA,; S. Ole Warnaar, University of Queensland, AUS; Nicholas Witte, Victoria University of Wellington, NZ.
    Brief Description:
    Special Functions-these include orthogonal polynomials, generalized, basic and elliptic hypergeometric functions, their analogues on root systems, finite fields, modular functions and more-is a field that is constantly evolving and has been a topic in classical mathematics for several centuries. New fundamental properties, identities and interconnections are constantly being discovered about these functions, including in representation theory, algebraic geometry, mathematical physics, number theory and combinatorics. Some recent advances in the theory of special functions are the link between elliptic hypergeometric integrals and supersymmetric indices in quantum field theory, beta and Selberg-type integrals in conformal field theory and the AGT conjecture, and the use of symmetric functions, such as Hall-Littlewood polynomials, in the representation theory of affine Lie algebras and W-algebras.

      The plan is to bring together a number leading experts working in the theory of special functions to discuss recent trends and developments in the field.

  • Stochastic and Deterministic Inverse Problems
    Marie Graff, University of Auckland, NZ,; Tiangang Cui, University of Sydney, AUS; Bamdad Hosseini, University of Washington, USA.
    Brief Description:
    The integration of complex data sets into large-scale computational models is a central challenge in modern applied mathematics. This challenge is ubiquitous across various application areas within science and engineering, including geosciences, biological systems, astrophysics, meteorology, aerospace, and subsurface flow. At the heart of this challenge often lies an inverse problem: converting indirect data into characterisations of unknown model parameters such as source terms, initial or boundary conditions, model structure, and physical coefficients.

      Our session brings together leading experts and emerging scholars in deterministic and stochastic inverse problems to discuss the latest developments, challenges, and breakthroughs. We will focus on the mathematical foundations and algorithmic strategies for solving inverse problems, including classical perspectives such as well-posedness and modern developments in scientific machine learning and uncertainty quantification.

  • Stochastic Differential Equations
    Ngan Le, Monash University, AUS; Beniamin Goldys, University of Sydney, AUS.
    Brief Description:
    The theory of stochastic, ordinary and partial, differential equations is motivated by manifold applications in sciences and engineering, including such phenomena as wave propagation in random media, turbulence, stochastic particle systems arising in physics, social sciences and population dynamics, and filtering and optimal control of stochastic systems.

      The Stochastic Differential Equations session will foster international collaboration of researchers in some of the most active and promising areas of stochastic differential equations with a strong focus on their theory and numerical analysis. Another important goal of the session will be to expose young researchers and postgraduate students to the most recent developments in theory, numerical methods and applications of stochastic differential equations.

  • Algebraic Combinatorics and Matroids
    Organisers: Graham Denham, Western University, Canada; Christin Bibby (Louisiana State University, USA); Zsuzsanna Dancso (University of Sydney, AUS)
    Brief Description: Algebraic combinatorics is a topic concerned with orderings, symmetries, and enumeration of discrete and finite structures. It is integrated with the fabric of a range of other research areas such as algebraic geometry, representation theory, commutative algebra, and mathematical physics. The aspects related to hyperplane arrangements and matroids are particularly timely, in view of June Huh’s 2022 Fields Medal citation.
  • Applied and Computational Topology
    Organisers: Nicholas Scoville, (Ursinus College, USA); Katharine Turner, (Australian National University, AUS)
    Brief Description: This special session will be devoted to all aspects of applied and computational topology. Specific themes include but are not limited to topological data analysis, robotics, dynamical systems, pure computational topology, image processing, persistence, theoretical and applied computer science, visualization, and theoretical foundations of applied and computational topology.
      We hope to feature a broad and diverse group of talks that strike a balance between the theory, applications, and implementation.
  • Computational Methods and Applications of Dynamical Systems
    Organisers: Hinke Osinga, University of Auckland, NZ,; Warwick Tucker, Monash University, AUS; Zachary Kilpatrick, University of Colorado, Boulder, USA.
    Brief Description: The theme is the development and application of computational methods for nonlinear phenomena that are beyond the reach of dynamics simulations: investigating invariant manifolds, discontinuity-induced bifurcations, or trajectories that are extremely sensitive to initial conditions.
      Presentations will range from the theoretical end, involving computer-assisted proofs, to the applied end, involving case studies based on experimental data.
  • Computations and applications of algebraic geometry and commutative algebra
    Organisers: John Cobb, University of Wisconsin, USA,; Anand Deopurkar, Australian National University; Sione Ma’u, University of Auckland, NZ; Hal Schenck, Auburn University, USA.
    Brief Description: The goal of this meeting is to bring together experts in algebraic geometry and commutative algebra, with an emphasis on computations and applications.
  • Recent developments in data science and machine learning
    Organisers: Han Feng, Department of Mathematics, City University of Hong Kong; Xin Guo, School of Mathematics and Physics, University of Queensland, AUS; Yiming Ying, School of Mathematics and Statistics, University of Sydney, AUS,; Ding-Xuan Zhou, School of Mathematics and Statistics, University of Sydney, AUS.
    Brief Description: The session provides a multidisciplinary platform for researchers in data science and machine learning to foster dynamic interdisciplinary dialogue among mathematicians, statisticians, and computer scientists. Throughout the session, participants will delve into recent breakthroughs and developments in both methodological, theoretical and practical aspects of modern data science that have reshaped the field. Insights from presentations and discussions will illuminate emerging trends in a wide spectrum of areas in data science including statistical learning, computational optimization, approximation techniques, and learning theory.
  • Differential delay equations and their applications
    Organisers: Anatoli Ivanov, Pennsylvania State University, USA; Bernd Krauskopf, University of Auckland, NZ; Sergiy Shelyag,, Flinders University, AUS.
    Brief Description: Delay differential (and, generally, functional differential) equations (DDEs) and their systems appear in natural and artificial phenomena, when the behavior of a system explicitly depends both on its current state and its history in some functional form. Examples include but not limited to population growth, infection spreads, epidemics and pandemics, physiological and neurophysiological processes, business cycle models in economics, decision making, feedback loops and control systems involving sensors and actuators in engineering.
      We propose a special session on delay differential equations, dynamical systems with retardation, and their applications in modelling real world phenomena, such as biology and physiology, decision-making and control problems.
      The aim of the session is to combine the expertise of pure, applied and computational mathematicians to explore and advance the current state of theory and applications of delay-differential equations.
  • Functional Analysis and partial differential operators
    Organisers: Daniel Daners, University of Sydney, AUS,; Tom ter Elst, University of Auckland, NZ.
    Brief Description: The aim is to bring together researchers working in the connected fields of Analysis and Partial Differential Operators. The field PDE is very broad and in this session we wish to focus on the analysis side of PDE and on the PDE with Functional Analytic connections.
  • Groups and Geometry
    Organisers: Kai-Uwe Bux (University of Bielefeld), Germany; James Parkinson (University of Sydney), AUS; Jeroen Schillewaert (University of Auckland), NZ,; Anne Thomas (University of Sydney), AUS.
    Brief Description: Jacques Tits has shown how geometric objects (buildings) can be employed in the study of algebraic groups; and these methods extend to thestudy of groups over local and global fields and arithmetic subgroups therein. In addition, building like complexes have been employed in a similar manner to understand groups such as the (outer) automorphism groups of free groups or mapping class groups of surfaces. Thus, buildings are key examples for spaces encountered in geometric group theory exhibiting important features such as non-positive curvature.
      The session aims at bringing together early career researchers and leading experts on buildings and related structures. The meeting will foster discussion about which research avenues appear promising in light of recent progress and breakthroughs.
  • Groups, actions and computations
    Organisers: Eamonn O’Brien University of Auckland, NZ; Heiko Dietrich, Monash University, AUS; Peter Brooksbank Bucknell University, USA.
    Brief Description: This session will be devoted to groups and related algebraic structures with a particular focus on computational results, tools, and applications. The program will feature talks from researchers at various career stages with topics drawn from permutation groups, algebraic isomorphism problems, geometric group theory, finite geometries, multilinear algebra, and group-based cryptography.
  • Industrial Mathematics
    Organisers: Barbara Keyfitz, Ohio State University, USA; Melanie Roberts, Griffith University, Australia; Steve Taylor, University of Auckland, New Zealand,
    Brief Summary: This session aims to highlight the role of applied and industrial mathematics in solving challenges across industry and government sectors and the advancements to mathematics driven by industrial applications. The focus will be on showcasing successful projects, methodologies, and case studies where mathematical modelling, simulation, optimization, and data analytics have been instrumental in addressing real-world problems and where real-world problems have motivated mathematical developments.

      The session will emphasize the importance of interdisciplinary collaboration between mathematicians, engineers, scientists, health, and other domain experts from industries and government agencies. It will also explore the opportunities in translating mathematical research into practical applications that address the needs faced by end users in industry and government.
      Topics may include, but are not limited to: Mathematical modelling and simulation in industrial processes, environmental management and sustainability, biological and medical systems; optimization techniques for resource allocation and scheduling, data-driven decision-making in government policy and planning, risk assessment and management in finance and insurance, machine learning and artificial intelligence in industry and government applications, mathematical methods for cybersecurity and network security.
    We invite researchers, practitioners, and policymakers from academia, industry, and government to submit abstracts for presentations that demonstrate how applied and industrial mathematics can contribute to solving real-world problems and improving decision-making processes in industry and government.
      This session aims to foster discussion and collaboration, leading to innovative solutions and impactful outcomes that benefit society as a whole.

  • Mathematical methods in the wave theory
    Organisers: Yury Stepanyants,; Fabien Montiel, Otago University, NZ; Timothy Marchant, University of Wollongong, AUS; Simon Clarke, Monash University, AUS.
    Brief Description: The symposium will focus upon the following topics:
    Mathematics of waves in seas covered by ice; Theory of water wave scattering in random and regular media; Developments in the soliton theory; Soliton-like structures in non-integrable systems; Rogue waves and collapses in continuous media; Experimental observations of solitary waves in laboratories and in the nature.
      The main thrust of the symposium is to discuss contemporary mathematical methods and achievements in the water-wave theory, the soliton-like structures occurring in various physical contexts and to break down the artificial walls separating researchers working in different fields. Theoretical, numerical, and experimental works are welcomed.
  • Mathematical modelling in continuum mechanics
    Organisers: Brendan Harding, Victoria University of Wellington, NZ; Yvonne Stokes, University of Adelaide, AUS; Rebecca Hardenbrook, Dartmouth College, USA.
    Brief Description: Continuum mechanics plays a pivotal role in modelling the macroscopic behaviour of materials. The applications are vast and span a wide range of scales, for example microscale fluid phenomena, stress on engineered structures, break up of sea ice, weather forecasting, and galaxy formation. This special session will provide a platform for researchers to explore and discuss recent advancements in mathematical approaches to continuum mechanics or new problems in continuum mechanics that benefit from mathematical modelling.
      The session aims to facilitate collaboration and knowledge exchange among researchers working at the intersection of mathematics and continuum mechanics, fostering the dissemination of cutting-edge research and the exploration of new directions in this interdisciplinary field. Topics include, but are not limited to: studies of elasticity and plasticity of solids, the motion of Newtonian and non-Newtonian fluids/gases, and multi-phase problems involving fluid-structure interaction or free surfaces.
      Researchers are invited to submit original contributions that concern the application of mathematics to continuum mechanics. Submissions may include theoretical developments, computational studies, applications of mathematical models in new problems, and comparison of models with experiments.
  • New directions in pattern formation
    Organisers: Priya Subramanian, University of Auckland NZ,
    Brief Description: This will complement a satellite workshop proceeding the conference which will have introductory talks on pattern formation with three main focus directions, (i) modelling vs characterisation of patterns, in (ii) discrete vs continuous systems, of (iii) active vs. passive systems that form multi- dimensional patterns.
  • Recent advances in mathematical fluid dynamics
    Organisers: Richard Clarke, University of Auckland, NZ; Mimi Dai, University of Illinois, USA,;
    Kengo Deguchi, Monash University, AUS; Igor Kukavica, University of Southern California, USA; Wojciech Ozanski, Florida State University, USA.
    Brief Description: The equations of fluid motion, derived over a century ago, are a source of enormous challenges and exciting problems for mathematicians. At large velocities, fluid flows become seemingly chaotic, but nevertheless possess some structure. It is widely believed that such flows, called turbulent and often observed in nature, still satisfy the equations of motion (Navier-Stokes equations), but are difficult to construct or study mathematically.
      In recent years, mathematical fluid dynamics has been highlighted by numerous breakthroughs regarding classical well-posedness issues and phenomenological theory of turbulence. These include significant advancements on the following topics for many fluid equations: unique solvability, singularity formation, stability and instability, anomalous dissipation of energy, etc. In the advancements, new analytical tools have emerged from other fields of mathematics and even physics.
      Through this special session, we aim to bringing together experts in mathematical fluid mechanics to discuss recent exciting developments in these aforementioned directions from the mathematical point of view, as well as their relevance to turbulence. We plan to take advantage of this unique opportunity provided by the joint meeting to extend academic networks among US, New Zealand, and Australia. We will also promote diversity and inclusion in our research field through this meeting.
  • Structural aspects of matroids and graphs
    Organisers: Kevin Grace, University of South Alabama, USA.; Andrei Pavelescu, University of South Alabama, USA.
    Brief Description: This session will consider topics within the areas of structural matroid theory and graph theory. Topics considered will include (but will not be restricted to) matroid minors, matroid representability, matroid connectivity, graph minors and treewidth, delta matroids, embeddings of graphs in topological surfaces, and signed graphs.
  • Optimisation
    Organisers: Minh N. Dao, RMIT University, AUS,; Andrea Raith, University of Auckland, NZ; Matthew K. Tam, University of Melbourne, AUS; Golbon Zakeri, University of Massachusetts, Amherst, USA.
    Brief Description: Mathematical optimisation is the study of using mathematics to make better decisions when faced with competing options. This special session will focus on new mathematical and computational developments and their applications in all areas of continuous and discrete optimisation. Submissions related to applications of optimisation in data science, as well as data science applications in optimisation, are also welcome.
  • Computational Mathematics
    Organisers: Quoc Thong Le Gia, UNSW, Sydney, AUS,; Bishnu Lamichhane, University of Newcastle, AUS; Ricardo Ruiz Baier, Monash University, AUS; Mahadevan Ganesh, Colorado School of Mines, USA; Stephen Joe, University of Waikato, NZ
    Brief Description: 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.
  • Engagement with mathematics through communication and outreach
    Organisers: Sean Gardiner, University of New South Wales, AUS, –; Yudhi Bunjamin University of New South Wales, AUS.
    Brief Description: Many recent world events have further emphasised the importance of furthering public understanding of mathematics and the role that mathematical thinking plays in the daily lives of all people, including those not directly working in the field. Additionally, even those who regularly engage with mathematics can discover more about what it means to be a mathematician through outreach initiatives. It is therefore important that the mathematical community continues to be invested in the role that mathematicians have in engaging people with the discipline.
      This special session will serve as an opportunity to discuss recent efforts to engage more audiences with mathematics through communication and outreach, and to share ideas, results, outcomes, and challenges encountered in outreach development and delivery. This joint meeting is a particularly good opportunity to explore how mathematics engagement is encouraged in different contexts, and for fostering international collaboration in this area.
  • Mathematics of nonlinear diffusion processes
    Organisers: Eliot Fried, Okinawa Institute of Science and Technology, Japan; James McCoy, University of Newcastle, AUS,; Glen Wheeler, University of Wollongong, AUS.
    Brief Description: Nonlinear diffusion processes, including higher order cases, have significant applications in physics, engineering and beyond, such as the thermal grooving in metals, the growth of crystals and transport in porous media. Their mathematical models are also closely related to those for shapes of biomembranes, including the red blood cell.
      The goal of this session is to convene key experts at various career stages to present the latest developments in this area concerning mathematical understanding and applications of the models. The aim is to promote discussion and collaboration to propel further advances in the field. Specific topics covered are expected to include curve diffusion flow and surface diffusion flow, possibly along with other related flows like the elastic flow of curves and the Willmore-Helfrich flow of surfaces. Special solutions including self-similar solutions, long time existence of solutions, stability and singular behaviour will also be addressed.
  • Microlocal analysis and inverse problems
    Organisers: James Webber, Harvard University and Brigham and Women’s Hospital, USA,; Todd Quinto, Tufts University, USA.
    Brief Description: Microlocal analysis studies more broadly the singularities of generalised functions and comprises techniques developed in recent decades that relate to the study of, e.g., pseudo differential operators, wavefront sets, and Fourier operators. These techniques have been employed fruitfully in the recent inverse problems literature, e.g., to identify and enhance machine learning based image construction methods.
      In this special session, we aim to bring together some of the best and upcoming researchers in microlocal analysis and inverse problems to present the leading developments in the field. Topics may include semiclassical analysis, generalised Radon transforms, local resolution analysis, uncertainty quantification, and machine learning, as well as applications to imaging sciences, astronomy, and materials characterisation.
  • Discrete and continuous integrable systems: geometry analysis and applications
    Organisers: Andrei Prokhorov, University of Michigan, USA; Pieter Roffelsen, University of Sydney, AUS,
    Brief Description: This session will bring together researchers across the oceans working in the field of integrable systems in all of its flavours, including but not limited to asymptotic analysis, billiards, differential and difference equations, orthogonal polynomials and random matrix theory, Riemann-Hilbert theory, symmetries and algebro-geometric aspects of integrability, applications.