On 24th June 2015, Professor Stephen Power introduced Professor Nalini Joshi of the University of Sydney and drew attention to her role as President of the Australian Mathematical Society and her diverse research in differential equations and integrable systems.
Professor Joshi then lectured on "When Applied Mathematics Collided with Algebra". She described how the discrete Painlevé equations can be introduced via affine Weyl groups, and a dynamical system involving tessellation of the plane by root systems.
She then described how the first Painlevé differential equation describes electrolysis and the 2D Ising model. The solutions are transcendental functions which have a relatively simple description through a repeated blowup procedure on the space of initial values. Analogously, the discrete Painlevé equations can be classified geometrically. There were some questions from the audience relating to the algebraic geometry of these solutions.
The lecture was followed by a reception at which the audience spoke with Nalini Joshi in an informal setting.
