My main research interest is in computational topology and geometry. I work on the underlying mathematics, algorithms, and applications to scientific problems.
A link to diamorse: a code package for topological data analysis of digital images. Diamorse will compute a discrete Morse vector field, topologically dual skeletons and partitions, and persistent homology from 2D and 3D greyscale image data.
Take a look at EPINET: a web database of periodic network structures.
The hyperbolic crystallography of the cubic genus-3 triply periodic minimal periodic surfaces is here.
My PhD thesis (2000) explored the mathematical foundations for computing topological information from data.
I'm part of the 1st year physics teaching team for PHYS1101, and teach the group theory part of the physics honours/masters course PHYS4301.
I'm actively seeking outstanding Honours, Masters and PhD students to conduct projects in applied geometry and topology. See the Available projects tab and contact me for further details.
I supervise a few undergraduate research projects each year with PhB and advanced studies students from Physics, Mathematics, and Engineering. Recent examples include "Investigating the relationship between curvature and deflection of thin sheets", "Symmetries of graphs on surfaces", "Polyhedral models of periodic minimal surfaces"
My past lecturing at ANU has included the Linear Algebra half of MATH1115, the basics of crystallography and thermal properties of lattices for PHYS3032 and a special topics course on Applied Topology for MATH4349.
Grants and awards
ARC Future Fellow 2014-2019 Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials.
I've worked with five artists in residence from the ANU School of Art under the ANU Vice-Chancellor's College Artist Fellowship scheme: Erica Seccombe, Julie Brooke, Al Munroe, Susan Buret, Alex Gillespie.
Erica and I published an essay "3D X-ray art" about the techniques used in her work in the Australian Physics magazine, Jan 2015.
Art student Emily O'Neill made the piece "Porous" for the exhibition Insight Out, Kambri 2021.
Physics has 150+ HDR students enrolled and a part of the HDR convenor team, I provide both formal and informal support to students and their supervisors.
Editor for the Journal of Applied and Computational Topology
This Springer journal publishes research that applies algebraic and combinatorial topology to problems in science and engineering. It serves both mathematicians and users of mathematical methods.
Asia-Pacific Applied Topology and Geometry Seminar series
I run an online seminar series with Yasuaki Hiraoka (Kyoto), Emerson Escolar (Kobe), and D Yogeshwaran (ISI, Bangalore). Videos of past talks are available online.
In November 2020, I was interviewed by Prof Liz Bradley as part of the inaugural interview series for the AATRN (Applied Algebraic Topology Research Network).
BSc (Hons I and University Medal) in Mathematics, ANU, 1994
PhD in Applied Mathematics, University of Colorado, Boulder, 2000
Former Honours and MSc students
- Nicholas Bohlsen (H1, 2023) Applications of Computational Topology to Fusion Science (with Matthew Hole, MSI)
- Thomas Burnett (H1, 2023) Persistent Homology Shape Recognition with Applications in Fingerprint Biometrics (with Katharine Turner, MSI)
- Olin Gao (H1, 2023) Crystallographic Groups from the Orbifold Perspective
- Jency Jiang (MSc HD, 2022) Analysing retinal images using (extended) persistent homology (with Katharine Turner, MSI)
- Nicholas Bermingham (H1, 2022) Detecting and Quantifying Approximate Symmetries Using the Extended Persistent Homology Transform (with Katharine Turner, MSI)
next: PhD student at The Ohio State University
- Adam Onus (H1, 2020) Persistent homology of periodic point data (with Martin Helmer, MSI)
next: PhD student at Queen Mary University, London
- Bettina Hill (H2A, 2020) Shape analysis of leaf silhouettes (with Katharine Turner, MSI)
next: Bureau of Meteorology
- James Morgan (H1, 2020) Central Limit Theorems for Euler Characteristic Processes on Random Flag Complexes (with Katharine Turner, MSI)
next: PhD at University of Sydney
- Kelly Maggs (H1, 2019) Discrete Morse theory and persistent homotopy
next: MPhil at ANU, PhD at EPFL, Switzerland
- Joel Martin (H2A, 2018) Topological Crystallography
next: Bureau of Meteorology
- Kassel Hingee (H1, 2008) Morse-Smale functions and image analysis
next: PhD at UWA, postdoc at the Sustainable Farms Project, ANU
Former HDR students
- Kelly Maggs (MPhil, 2020) Topological data analysis for fuzzing (External scholarship funding)
now a PhD student at EPFL, Switzerland
- Sahar Masoudian (MPhil 2020) Computable invariants of entangled periodic structures
now a PhD student at UNSW
- Amit Singh (PhD, 2018) Dynamics properties, formation and shape of leaves (Co-supervised with Adrienne Nicotra)
now working in the public service
- Toen Castle (PhD, 2013) Modes of entanglement in polyhedral graphs(Co-supervised with Stephen Hyde)
Lecturer at La Trobe University, Victoria
- Myfanwy Evans (PhD, 2010) Three-dimensional entanglement: knots, knits and nets (Co-supervised with Stephen Hyde)
Professor at Potsdam University, Germany