Diarmuid Crowley

Diarmuid Crowley is an Associate Professor in Pure Mathematics in the School of Mathematics and Statistics at the University of Melbourne. His research specializes in the differential topology of high-dimensional manifolds and surgery theory. Key areas of interest include the topological residues of geometric structures such as G₂-structures and contact structures, 7-manifolds, the foundations of surgery, spaces of diffeomorphisms and mapping class groups, exotic spheres, and the Gromoll filtration. Additional focuses encompass algebraic topology, differential topology, and the surgery classification of manifolds. He is a member of the Topology Research Group within the Pure Mathematics Research Group and co-leads the 2022 ARC Discovery Project titled 'Topology in seven dimensions' with Johannes Nordström from the University of Bath.

Crowley coordinates the Pure Mathematics Seminar and Topology Seminar at the University of Melbourne. He serves on the Career Development Committee, Executive Committee, Management Committee, Mathematics and Statistics Fund Committee, and UGS Committee. He supervises several postgraduate students, including current PhD candidates Tianqi Feng, Jayden Hammet, Riley Moriss, Chandan Singh, and John Stewart. Past PhD supervisions include Songqi Han on 'Stable Parametrised H-Cobordism Theorem for Smooth Manifolds with Tangential Structure' and Csaba Nagy on 'The classification of 8-dimensional E-manifolds'. He also supervises current MSc students Isla Wen Cong Lim, Matthew Ryan on 'Spherical Classes, Immersions and Embeddings', and Anthony Tianqi Wu on 'Normal Fibration of a Finite CW-complex', among past Honours and MSc students such as Tianqi Feng, Jayden Hammet, and Blake Sims. His publications feature prominently in top journals. Key works include 'New invariants of G₂-structures' with J. Nordström (2015, 87 citations), 'A classification of S³-bundles over S⁴' with C.M. Escher (2003, 74 citations), 'The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature' with T. Schick (2013, 64 citations), 'The classification of 2-connected 7-manifolds' with J. Nordström (2019, 43 citations), 'The smooth classification of 4-dimensional complete intersections' with C. Nagy (2025), 'Turning vector bundles' with C. Nagy, B. Sims, and H. Yang (2024), and 'Infinite homotopy stable class for 4-manifolds with boundary' with A. Conway and M. Powell (2023).

Professional Email: dcrowley@unimelb.edu.au