Welcome from Professor Gary Froyland
School of Mathematics & Statistics
UNSW, 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 , the atmosphere, and granular flows, using models and observational data. This sketches some my applied dynamics research, and this 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 Jason Atnip
Dr Jason Atnip
(ARC Research Fellow with A/Prof. Cecilia Gonzalez-Tokman)
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 “Data, models and transitions - bottom-up and top-down approaches in computational neuroscience”. 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 UNSW, 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 Kühl Oliveira
Kevin Felipe Kühl Oliveira
(PhD student)
Research Interests: Random Dynamical Systems; Scientific Machine Learning; Multiscale Modelling; Operator Theory; Spectral Methods.
Yat Long (Luca) Lee
Yat Long (Luca) Lee
(PhD student)
I am a PhD student in Mathematics at UNSW. My work focuses on applying differential-geometric techniques and concepts to study problems arising from dynamical system. Aside from researching mathematics, I am also passionate about teaching and sharing mathematics.
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 Völkner
Kathrin Völkner
(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 UNSW (2006-)
Research Fellows
- Dr Michelle Dunbar (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) (ԴǷLecturer at UNSW Sydney)
- Konstantinos Sakellariou (2017-2018) ARC Discovery Project (with O. Junge and A. Quas) (now Researcher at )
- Davor Dragičević (2015-2017) ARC Discovery Project (with O. Junge and A. Quas) (ԴǷ)
- Cecilia González-Tokman, (2012-2015) ARC Discovery Project (with M. Dellnitz and A. Quas) (ԴǷ)
- Andy Hammerlindl, (2012-2015) ARC Discovery Project (with G. Gottwald) (ԴǷ)
- Naratip Santitissadeekorn, (2008-2011) ARC Centre of Excellence MASCOS (ԴǷ)
- Simon Lloyd, (2007-2010) ARC Discovery Project (with M. Dellnitz and A. Treguier) (ԴǷ)
- Irina Dumitrescu, (2006-2009) ARC Linkage Project (with N. Boland) (ԴǷ)
PhD students
- Michael C. Denes PhD 2023, UNSW.
ճ:Transport and mixing by persistent and materially coherent ocean structures.(ԴǷ) - Christopher P. Rock PhD 2022, UNSW.
ճ:Extracting features from eigenfunctions: higher Cheeger constants and sparse eigenbasis approximation.(ԴǷ) - Harry Crimmins PhD 2021, UNSW.
ճ:Statistical stability for deterministic and random dynamical systems.(ԴǷ) - Fadi Antown PhD 2020, UNSW.
ճ:Linear response in dynamical systems: Optimisation and finite-time coherent sets. (now Decision Scientist at ) - Eric Kwok PhD 2018, UNSW.
ճ:Dynamic isoperimetry on graphs and weighted Riemannian manifolds.(ԴǷ). - Thomas Watson PhD 2016, UNSW.
ճ:On Aspects of Numerical Ergodic Theory: Stability of Ulam's Method, Computing Oseledets Subspaces, and Optimal Mixing.(ԴǷ) - Mehrdad Heidari, PhD 2015, UNSW.
ճ:Quantification of Geological Uncertainty and Mine Planning Risk using Metric Spaces.(ԴǷ) - Robyn Stuart, PhD 2014, UNSW.
ճ:Metastable sets in open dynamical systems and substochastic Markov chains. (ԴǷ) - Stephen Maher, PhD 2014, UNSW.
ճ:The Application of Recoverable Robustness to Airline Planning Problems. (now an ) - Amirah Rahman, PhD 2013, UNSW.
ճ:Freight train scheduling on a single line network. (now Senior Lecturer at the ) - Michelle Dunbar, PhD 2012, UNSW.
ճ:Minimising Propagated Delay in an Integrated Aircraft Routing and Crew Pairing Framework. (ԴǷLecturer, UNSW) - Ognjen Stancevic, PhD 2011, UNSW.
ճ:Escape and Metastability in Deterministic and Random Dynamical Systems. (now Executive Manager, Enterprise Risk Analytics and Visualisation, , Sydney) - Dalia Terhesiu, PhD 2009, UNSW.
ճ:On the approximation of finite and infinite equilibrium states and some aspects of Young towers with non-integrable return function. (ԴǷ) - Therese Keane, PhD 2009, UNSW (with J. Franklin).
ճ:Combat Modelling with Partial Differential Equations. (ԴǷ
Honours students
- Satvik Yadav, (Hons 2022), UNSW
- Ruiwen Zhong, (Hons 2022), UNSW
- Jack Hills (Hons 2022), UNSW Engineering with Prof. Tracie Barber
- Raymond Cheng, Hons 2020, UNSW
- Kevin Tian, Hons 2020, UNSW
- Christos Kollias, Hons 2019, UNSW
- Ben Madafiglio, Hons 2018, UNSW
- Chris Bladwell, Hons 2018, UNSW (now PhD student at UNSW)
- Harry Crimmins, Hons 2017, UNSW (now PhD student at UNSW)
- Daniel Picone, Hons 2017, UNSW (ԴǷ)
- Chris Rock, Hons 2017, UNSW (now PhD student at UNSW)
- Fadi Antown, Hons 2015, UNSW (now PhD student at UNSW)
- James Ross, Hons 2015, UNSW (ԴǷ)
- Jeremy Nugent, Hons 2014, UNSW (now PhD student at UNSW)
- Alec Gilbert, Hons 2013, UNSW (now postdoc at University of Heidelberg)
- Georgia Tsambos, Hons 2013, UNSW (now PhD student at UMelb)
- Andrew Ardill, Hons 2010, UNSW (ԴǷ)
- Ognjen Stancevic, Hons 2007, UNSW (now Executive Manager, Enterprise Risk Analytics and Visualisation, , Sydney)
- Ambros Gleixner, Hons 2006, UNSW (currently )
- Gina Choutis, Hons 2006, UNSW (currently )