Alan Carey is internationally renowned for original research in several distinct areas of pure mathematics, bridging analysis, geometry, topology and mathematical physics. He is particularly well known for his work on infinite dimensional groups and their application to quantum field theory. He is also a leading expert in spectral invariants of manifolds and has contributed strongly to the development of non-commutative geometry and its application to quantum–mechanical phenomena in solid state physics. Finally, Carey has written extensively on geometric structures in quantum field theory. Carey has also played a very strong leadership and nurturing role in Australian mathematics.