Hi, I'm Glen Wheeler.

I’m a mathematician at the University of Wollongong (Australia) working at the interface of geometry and analysis, with a particular focus on the dynamics of geometric evolution equations and higher-order flows. My PhD examined fourth-order geometric evolution equations. After that, I held an Alexander von Humboldt Research Fellowship at Otto von Guericke Universität Magdeburg with Prof. Dr. Hans-Christoph Grunau, continuing work on the dynamics of higher-order geometric flows.

I have just become an ARC Future Fellow (2026–2030) (FT250100880), developing new perspectives on the Cartan–Hadamard conjecture and on Yau’s problem about the equivalence of plane curves. I’m very excited to start the fellowship!

I am also a Chief Investigator on an ARC Discovery Project (2025–2027) (DP250101080) using mathematics to model bushfire dynamics. So far, this project has led to [1], [6], [8], and [14], including: a new model; the first existence–uniqueness results for that model; a study of moving fronts; and an analysis of how policy shapes the efficacy of bushfire response.

Previously, I was a Chief Investigator on an ARC Discovery Project (2015–2018) (DP150100375) focused on geometric flows. That grant catalysed much of my work on fourth-order flows—curve and surface diffusion, elastic/Willmore flows—as well as fully nonlinear second-order flows with non-smooth speeds and polyharmonic flows. It launched my research program and laid durable foundations for ongoing collaborations.

My work and teaching have been recognised with the biennial Peter Schwerdtfeger Award and the AustMS Early Career Teaching Excellence Award. I enjoy clear exposition, collaboration, and finding new connections between curvature, PDE, and real-world phenomena.

I have published specifically on the following topics (the numbers in brackets refer to papers in my list of publications):

1. Curve and surface diffusion ([5] (elliptic), [12], [26], [38], [44], [56], [57])
2. Families of fourth order flows ([43] (biharmonic heat equation (not geometric)), [49] (elliptic), [58], [59], [60])
3. Elastic, Willmore and Helfrich ([3] (elliptic), [4], [11], [16] (elliptic), [19], [30] (p-elastic), [47], [48], [51], [52])
4. Fire, crystals, wound healing and biomembranes ([1], [6], [8], [10], [14], [20], [36], [39], [50], [54], [55])
5. Chen’s conjecture and flow ([17], [33], [53])
6. Flows of arbitrary order ([21], [23], [34], [46]) in particular, of sixth order ([28], [35] (numerical), [37], [42])
7. Second-order flows ([9], [15], [25], [27], [32] (elliptic), [40], [41], [45])
8. Ideal flow ([24], [29], [31])
9. Entropy flow [13]
10. Sobolev curvature flow ([2], [18])
11. Invariant flows in fundamental geometries [7]

Links to my ORCiD, Google Scholar, and other external sites are in the header and footer of this page. If you wish to get in touch, please feel free to use my email.

Geometric Analysis Zulip Server. If you are interested in joining our Zulip server, please email geometricanalysiszulip@gmail.com. The YouTube channel for our seminar series aimed at PhD students and young researchers is also linked below. The homepage of the seminar is here.

Editorial work. I am on the editorial board for Journal of Evolution Equations (link) 2025-present, and the Bulletin of the Australian Mathematical Society (link) 2025-present. I have served as guest editor for the MATRIX Annals (link) for special issues attached to conferences held at MATRIX that I have organised.

Governance. I serve on the Executive of the Australian Association of Alexander von Humboldt fellows as the NSW representative, and have done so since 2021. (If you would like some advice regarding applications for Humboldt Fellowships, please let me know!) I am also recently elected to the Concil of the Australian Mathematical Society (from 2025). Locally, I have long held the chair of the School Education Committee (2016-2021, 2024-2025), leading curriculum reform and shaping service relationships. I have also served in a number of other minor governance roles, for instance as academic integrity officer and academic program director.

Phd Scholarships. I have supervised Scott Parkins (2017), Lachlan Macdonald (2019), Shuhui He (2019) ,Yuhan Wu (2021), Sam Cuthbertson (2025), and Lachlann O’Donnell (2025) to PhD completion. I am currently supervising Ben Whale. Are you interested in obtaining a PhD under my supervision? Then reach out! Right now, I have some special scholarships available connected to my recent future fellowship. Please take a look at the advertisement (link) for more information. If you are interested, let me know as soon as possible. For the scholarships, I am looking for students to start in 2026.