Dr Wheeler is an internationally recognised mathematician working at the interface of geometry and analysis, with a long-standing focus on higher-order geometric flows and an increasingly significant research program in non-local partial differential equations motivated by moving-front problems such as bushfire dynamics. He is currently ARC Future Fellow (FT250100880, 2026–2030) for the project New directions in geometric flows, and is also a Chief Investigator on the ARC Discovery Project Non-local PDE approach to moving fronts and bushfires (DP250101080, 2025–2027). His work combines foundational geometric analysis with mathematically rigorous models for physically and socially significant phenomena.

Dr Wheeler’s publication and citation profile is exceptionally strong by contemporary mathematical-sciences standards (mathematics is a low-citation field: 2–3 year impact factors of some of the most prestigious theoretical-mathematics journals are typically about 1, and publication rates of international high-achievers are often below one paper per year, see the IMU–ICIAM–IMS report on citation statistics). Dr Wheeler's public publications page (here) currently lists 68 outputs, including 50 refereed journal articles and a particularly strong 2025–2026 stream. Google Scholar currently (29th March 2026) records 869 citations, 505 citations since 2021, an h-index of 19, and an i10-index of 31. Recent work appears in leading journals including the Journal of the European Mathematical Society, Journal of Functional Analysis, Journal of Differential Equations, Archive for Rational Mechanics and Analysis, SIAM Journal on Applied Mathematics, Communications in Analysis and Geometry, Calculus of Variations and Partial Differential Equations, Physica D, and Advances in Calculus of Variations.

Dr Wheeler has supervised seven PhD students to completion and currently supervises Brad Rice, Ben Whale, Vindula Kumaranayake, and Dinh Dat. His research leadership is also reflected in national and international community building: he helps run the Australian Geometric PDE Seminar and the Geometric Analysis Zulip Server, runs the Geometric Analysis Seminar at UOW, serves on the editorial boards of the Journal of Evolution Equations, Bulletin of the Australian Mathematical Society, and Transactions in Pure and Applied Mathematics, and has organised major research programs at MATRIX in 2025 and 2026. His work and teaching have also been recognised further by an Alexander-von-Humboldt Research Fellowship, ARC Discovery Project DP150100375, the Peter Schwerdtfeger Award and the AustMS Early Career Teaching Excellence Award.