Welcome from Professor Gary Froyland
School of Mathematics & Statistics
麻豆社madou, Sydney
My research spans two areas: dynamical systems and optimization.
My dynamical systems research focusses on the interplay of probability and geometry in nonlinear and chaotic dynamical systems, and uses tools from ergodic theory, functional analysis, and differential geometry. In addition to fundamental mathematical research in dynamical systems, I have applied my research methods to analyse聽, the atmosphere, and granular flows, using models and observational data. This聽聽sketches some my applied dynamics research, and this聽聽is pitched at the general public.
My optimization research is focussed on decision making in large and complicated systems, sometimes in the presence of uncertain information. My research concerns new modelling approaches in mathematical programming, integer programming, and stochastic programming. These new approaches have been applied to strategic planning of open pit mines, scheduling of maritime crane fleets, and robust scheduling of aircraft and flight crews under uncertain disruption. Current work includes optimising lung cancer radiotherapy treatment.
Current Members
Postdoctoral Fellows
Dr Aleksandar Badza
Dr Aleksandar Badza
(ARC Research Fellow)
My research is focused primarily on analysis of dynamical systems. I specialise in the detection of Lagrangian coherent structures and almost invariant sets in a variety of idealised, simulated and real world velocity systems. I am also proficient in complex analysis, numerical methods, optimisation and statistics.
Dr Manu Kalia
Dr Manu Kalia
(Einstein Research Fellow)
PhD in 2022 titled 鈥Data, models and transitions - bottom-up and top-down approaches in computational neuroscience鈥. Manu is an applied mathematician by training, with research interests in computational and mathematical neuroscience, dynamical systems and bifurcation theory, network theory and the interaction of machine learning with dynamical systems.
Dr Matheus Manzatto de Castro
Dr Matheus Manzatto de Castro
(ARC Laureate Research Fellow)
I am a postdoctoral fellow at 麻豆社madou, working with Prof. Gary Froyland. I completed my PhD in Mathematics at Imperial College London under the supervision of Prof. Jeroen Lamb and Prof. Martin Rasmussen. My research interests are dynamical systems and Markov processes, specifically in the statistical properties of random dynamical systems, non-uniformly hyperbolic systems and absorbing Markov processes.
Dr Maxence Phalemphin
Dr Maxence Phalemphin
(ARC Laureate Research Fellow)
My research focus on ergodic theory, stochastic properties on dynamical systems and random graphs. Example of systems I am interested include complex structures over chaotic dynamical systems such as Lorentz gas, collision models or random environment as branching processes and random graphs.
PhD Students
Kevin Felipe K眉hl Oliveira
Kevin Felipe K眉hl Oliveira
(PhD student)
Research Interests: Random Dynamical Systems; Scientific Machine Learning;聽 Multiscale Modelling; Operator Theory; Spectral Methods.
Nicholas Peters
Nicholas Peters
(PhD student)
Hi, I'm Nick. I'm a PhD student from New Zealand and I started my PhD with Gary in 2024. For now, my thesis title is "operator based techniques for the analysis of dynamical systems" and currently I'm looking at methods for approximating the transfer and Koopman operators using data measured from the trajectory of a dynamical system. Outside of my studies, I also do fencing and taekwondo and I like painting.
Kathrin V枚lkner
Kathrin V枚lkner
(Einstein PhD student, joint with Prof. Dr Peter Koltai)
Honours Students
Redmond Mobbs
Redmond Mobbs
(Honours student)
Jahan Peiris
Jahan Peiris
(Honours student)
Former Members at 麻豆社madou (2006-)
Research Fellows
- Dr Michelle Dunbar聽(2015-2020) Cancer Australia and NHMRC Projects (with P. Bannon, J. Booth, F. Hegi-Johnson, R. O'Brien, C-C. Shieh, J-J. Sonke, and S. Vinod) (苍辞飞听Lecturer at 麻豆社madou Sydney)
- Konstantinos Sakellariou聽(2017-2018) ARC Discovery Project (with O. Junge and A. Quas) (now Researcher at聽)
- Davor Dragic虒evi膰聽(2015-2017) ARC Discovery Project (with O. Junge and A. Quas) (苍辞飞听)
- Cecilia Gonz谩lez-Tokman, (2012-2015) ARC Discovery Project (with M. Dellnitz and A. Quas) (苍辞飞听)
- Andy Hammerlindl, (2012-2015) ARC Discovery Project (with G. Gottwald) (苍辞飞听)
- Naratip Santitissadeekorn, (2008-2011) ARC Centre of Excellence MASCOS (苍辞飞听)
- Simon Lloyd, (2007-2010) ARC Discovery Project (with M. Dellnitz and A. Treguier) (苍辞飞听)
- Irina Dumitrescu, (2006-2009) ARC Linkage Project (with N. Boland) (苍辞飞听)
PhD students
- Michael C. Denes聽PhD 2023, 麻豆社madou.
罢丑别蝉颈蝉:听Transport and mixing by persistent and materially coherent ocean structures.听(苍辞飞听) - Christopher P. Rock聽PhD 2022, 麻豆社madou.
罢丑别蝉颈蝉:听Extracting features from eigenfunctions: higher Cheeger constants and sparse eigenbasis approximation.听(苍辞飞听) - Harry Crimmins聽PhD 2021, 麻豆社madou.
罢丑别蝉颈蝉:听Statistical stability for deterministic and random dynamical systems.听(苍辞飞听) - Fadi Antown聽PhD 2020, 麻豆社madou.
罢丑别蝉颈蝉:听Linear response in dynamical systems: Optimisation and finite-time coherent sets.聽(now Decision Scientist at聽) - Eric Kwok聽PhD 2018, 麻豆社madou.
罢丑别蝉颈蝉:听Dynamic isoperimetry on graphs and weighted Riemannian manifolds.听(苍辞飞听). - Thomas Watson聽PhD 2016, 麻豆社madou.
罢丑别蝉颈蝉:听On Aspects of Numerical Ergodic Theory: Stability of Ulam's Method, Computing Oseledets Subspaces, and Optimal Mixing.听(苍辞飞听) - Mehrdad Heidari, PhD 2015, 麻豆社madou.
罢丑别蝉颈蝉:听Quantification of Geological Uncertainty and Mine Planning Risk using Metric Spaces.听(苍辞飞听) - Robyn Stuart, PhD 2014, 麻豆社madou.
罢丑别蝉颈蝉:听Metastable sets in open dynamical systems and substochastic Markov chains.聽(苍辞飞听) - Stephen Maher, PhD 2014, 麻豆社madou.
罢丑别蝉颈蝉:听The Application of Recoverable Robustness to Airline Planning Problems.聽(now an聽) - Amirah Rahman, PhD 2013, 麻豆社madou.
罢丑别蝉颈蝉:听Freight train scheduling on a single line network.聽(now Senior Lecturer at the聽) - Michelle Dunbar, PhD 2012, 麻豆社madou.
罢丑别蝉颈蝉:听Minimising Propagated Delay in an Integrated Aircraft Routing and Crew Pairing Framework.聽(苍辞飞听Lecturer, 麻豆社madou) - Ognjen Stancevic, PhD 2011, 麻豆社madou.
罢丑别蝉颈蝉:听Escape and Metastability in Deterministic and Random Dynamical Systems.聽(now Executive Manager, Enterprise Risk Analytics and Visualisation,聽, Sydney) - Dalia Terhesiu, PhD 2009, 麻豆社madou.
罢丑别蝉颈蝉:听On the approximation of finite and infinite equilibrium states and some aspects of Young towers with non-integrable return function.聽(苍辞飞听) - Therese Keane, PhD 2009, 麻豆社madou (with J. Franklin).
罢丑别蝉颈蝉:听Combat Modelling with Partial Differential Equations.聽(苍辞飞听
Honours students
- Satvik Yadav, (Hons 2022), 麻豆社madou
- Ruiwen Zhong, (Hons 2022), 麻豆社madou
- Jack Hills聽(Hons 2022), 麻豆社madou Engineering with Prof. Tracie Barber
- Raymond Cheng, Hons 2020, 麻豆社madou
- Kevin Tian, Hons 2020, 麻豆社madou
- Christos Kollias, Hons 2019, 麻豆社madou
- Ben Madafiglio, Hons 2018, 麻豆社madou
- Chris Bladwell, Hons 2018, 麻豆社madou (now PhD student at 麻豆社madou)
- Harry Crimmins, Hons 2017, 麻豆社madou (now PhD student at 麻豆社madou)
- Daniel Picone, Hons 2017, 麻豆社madou (苍辞飞听)
- Chris Rock, Hons 2017, 麻豆社madou (now PhD student at 麻豆社madou)
- Fadi Antown, Hons 2015, 麻豆社madou (now PhD student at 麻豆社madou)
- James Ross, Hons 2015, 麻豆社madou (苍辞飞听)
- Jeremy Nugent, Hons 2014, 麻豆社madou (now PhD student at 麻豆社madou)
- Alec Gilbert, Hons 2013, 麻豆社madou (now postdoc at University of Heidelberg)
- Georgia Tsambos, Hons 2013, 麻豆社madou (now PhD student at UMelb)
- Andrew Ardill, Hons 2010, 麻豆社madou (苍辞飞听)
- Ognjen Stancevic, Hons 2007, 麻豆社madou (now Executive Manager, Enterprise Risk Analytics and Visualisation,聽, Sydney)
- Ambros Gleixner, Hons 2006, 麻豆社madou (currently聽)
- Gina Choutis, Hons 2006, 麻豆社madou (currently聽)