Sydney Dynamics Group




SDG workshop: Dynamical systems - theory and application, Blackheath, Blue Mountains, 6-10 November 2017



The SDG was founded in January 2007 as a cooperation of faculty members between two of the major universities in Sydney, Australia, the University of New South Wales (UNSW) and the University of Sydney (USyd). The group's research missions span topics in pure and applied dynamical systems, ranging from algebraic dynamics, ergodic theory, and Hamiltonian dynamics to rhythms in physiological systems, time series analysis, geophysical fluid dynamics and statistical mechanics.

    Members of the group:

  • Eduardo Altmann (USyd, Maths): Hamiltonian systems, transient chaos, extreme events, complex networks
  • Holger Dullin (USyd, Maths): Hamiltonian systems, rigid body dynamics with applications in biomechanics, topology of integrable systems, semiclassical quantization, volume preserving mappings
  • Chris Angstmann (UNSW, Maths): pattern formation, biomathematics, anomalous diffusion
  • Sasha Fish (USyd, Maths): ergodic theory, applications of dynamics to number theory
  • Gary Froyland (UNSW, Maths): smooth and numerical ergodic theory, applications to atmospheric and oceanic flows
  • Dave Galloway (USyd, Maths): solar and geodynamo modelling
  • Ben Goldys (USyd, Maths): stochastic partial differential equations, analysis on infinite-dimensional spaces, long time behaviour of solutions to stochastic ordinary and partial differential equations, optimal control
  • Georg Gottwald (USyd, Maths): geophysical fluid dynamics, pattern formation in biological and chemical systems, nonlinear time series analysis
  • Ray Kawai (USyd, Maths): statistics and numerical methods for stochastic differential equations, mathematical ecology, mathematical finance, optimization
  • Shane Keating (UNSW, Maths): mixing and stirring in geophysical turbulence, satellite altimetry, ocean state estimation, eddy parameterization
  • Peter Kim (USyd, Maths): mathematical biology, cancer modelling, agent-based models
  • Charlie Macaskill (USyd, Maths): geophysical fluid dynamics, especially vortex dynamics and internal waves, acoustics in complex and random media with applications in biomedical ultrasound, mathematical theory of combustion
  • Robert Marangell (USyd, Maths): dynamical systems, stability of nonlinear waves
  • Gary Morriss (UNSW, Physics): statistical mechanics of nonequilibrium systems
  • Milena Radnovic (USyd, Maths): integrable systems, billiards
  • John Roberts (UNSW, Maths): discrete integrable systems, symmetry and time-reversal symmetry, algebraic dynamics
  • Geoff Vasil (USyd, Maths): geophysical and astrophysical fluid dynamics, multi-scale methods, pattern formation
  • Martin Wechselberger (USyd, Maths): invariant manifold theory, canard theory, geometric singular perturbation theory with applications to the nervous system and cell signalling

    Postdocs:

  • Jason Atnip (UNSW, Maths): ergodic theory, random dynamical systems, statistical limit theorems
  • Ian Lizarraga (USyd, Maths): geometric singular perturbation theory, slow-fast dynamical systems, coupled oscillators
  • Debopriya Mukherjee (USyd and UNSW, Math): stochastic PDEs and optimal control of fluids
  • Konstantinos Sakelleriou (UNSW, Maths): numerical transfer operator methods, finite-time coherent sets, nonlinear time series analysis
  • Lachlan Smith (USyd, Maths): chaotic advection, piecewise isometries, mixing and transport, synchronization

    Graduate students:

  • Fadi Antown (UNSW, Maths): optimal linear response, stochastic dynamics, finite-time coherent sets
  • Madeleine Cartwright (USyd, Math): synchronization in power grids
  • Harry Crimmins (UNSW, Maths): stability and rigorous approximation of statistical limit laws
  • Mitch Curran (USyd, Maths): Maslov index in standing waves of the NLS equation on quantum graphs
  • Michael Denes (UNSW, Maths): finite-time coherent sets in ocean dynamics
  • Zeina Haidar (USyd, Maths): periodic trajectories of pseudo-integrable billiard within circle with a barrier
  • Brent Giggins (USyd, Maths): forecasting with bred vectors and covariant Lyapunov vectors
  • Zach Issa (USyd, Maths): Skorokhod embedding theorem with financial applications
  • Samuel Jelbart (USyd, Maths): non-standard GSPT
  • Farah El Rafei (UNSW, Maths): spin waves in nanowires under stochastic perturbations
  • Christopher Rock (UNSW, Maths): theory and numerics for the dynamic Laplacian
  • Tim Roberts (USyd, Math): stability of nonlinear waves and the Evans function
  • Camelia Tiplea (USyd, Math): pricing of American options
  • James Yang (USyd, Math): optimal control of slow fast systems
  • Caroline Wormell (USyd, Math): linear response theory in chaotic deterministic dynamical systems
  • Wenqi Yue (USyd, Math): model reduction for synchronization in complex networks

An eigenfunction of a transfer operator highlights gyres in the Weddell and Ross Seas off the Antarctic Coast (Froyland et al., Phys. Rev. Lett. 98:224503, 2007)



Escape time diagram of the Levitron, a levitating magnetic top (Dullin, Regular and Chaotic Dynamics 9, 255-264, 2004)



Effect of coarse-graining on the Kac ring model (Gottwald & Oliver, SIAM Review 51, 613-635, 2009)



    Seminars 2018:

  • 12/01/18: Daniel Lecoanet (Princeton) "Model hierarchies for computational data analysis"
  • 16/03/18: Amin Chabchoub (USyd) "Soliton and breather dynamics on the water surface"
  • 23/03/18: Justin Tzou (Macquarie) "Localised pattern dynamics and mean first passage time optimisation - analysis techniques and surprising connections"
  • 25/05/18: Dimitris Giannakis (Courant) "Spatiotemporal pattern extraction by spectral analysis of vector-valued observables"
  • 28/05/18: Andy Hammerlindl (Monash) "What is a blender?"
  • 01/06/18: Dmitry Pelinovsky (McMaster, Canada) "Standing waves on metric graphs"
  • 20/07/18: Caroline Wormell (USyd) "Classification of slow mixing formations in chaotic dynamics"
  • 03/08/18: Konstantin Clauß (TU Dresden) "Localization on fractals in open systems: A resonance eigenfunction hypothesis"
  • 24/08/18: Maxime Bombar (ENS Cachan) "The capacity of linear time invariant channels and delocalisation""
  • 31/08/18: Oliver Junge (TU München) "Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories"
  • 31/08/18: Bjorn Winckler (Imperial) "Instability of renormalization"
  • 07/09/18: Mason Porter (UCLA) "Spreading Processes on Networks"
  • 14/09/18: John Maclean (Adelaide) "Projected particle filtering"
  • 19/10/18: Edgar Knobloch (Berkeley) "Asymptotic techniques for flows with strong restraints: rapidly rotating convection"
  • 26/10/18: Ian Lizarraga (USyd) "Approximating slow manifolds with the computational singular perturbation method"
  • 21/11/18: Vladimir Zeitlin (ENS Paris) "Small is beautiful: understanding complex meteorological phenomena in tropics with simple mathematical models"

Maintained by Georg Gottwald