Harmonic analysis may be loosely defined as that branch of mathematics which has its origin in Fourier Series. In the past two centuries, it has become a vast subject with applications in areas as diverse as signals processing and quantum mechanics.

Interests of the harmonic analysis group range from classical problems to analysis on Lie groups.

Tony Dooley is a Principal Investigator with the ARC Centre of Excellence in the Mathematics and Statistics of Complex Systems (MASCOS) which has intersection with this group.

Michael Cowling's diverse interests include the theory of oscillatory and singular integrals, heat and other semigroups of operators, multipliers, heat kernels on Lie groups, uniformly bounded representations, lattices and rigidity. He is also studying harmonic analysis on discrete groups, operator algebras and, more recently, mathematical finance.

Tony Dooley has worked in lacunarity and L^p-multipliers on Lie groups, the theory of contractions of Lie groups, solvability of differential operators, intertwining operators, character formulae and the orbit method. His interests also include ergodic theory.

Garth Gaudry started life as a classical harmonic analyst and maintains his interests in multipliers of and singular integrals on the line. He subsequently extended many results in this area to the setting of Lie groups, notably solvable groups.

Ben Warhurst is working with Michael Cowling on contact and quasiconformal mappings on Carnot groups.

Norman Wildberger has worked on the orbit method and moment map on compact and nilpotent Lie groups. He has recently been developing the theory of hypergroups which impacts significantly in this area and also has applications to diophantine equations.