School of Mathematical Sciences Colloquium

All seminars will be held on a Friday, starting at 2:10 pm. The talks will be in Engineering North N132 and over Zoom.

To receive the Zoom link, please contact Judy Bunder.

Date Speaker Presentation
Friday 12 August
2:10 pm
Eng Nth N132
Serena Dipierro
University of Western Australia

Title: What is the (fractional) Laplacian and why is it useful for everybody?

Abstract: We will present some classical and contemporary trends in the research related to nonlocal equations and their impact in different fields.

Friday 19 August
2:10 pm
Eng Nth N132

Phil Broadbridge
La Trobe University

Title: Conditionally integrable reaction-diffusion systems with applications to fisheries

Abstract: Within a single-species fishery, for sustainability it is common to have a no-take-area. Within the NTA, the population is commonly represented by a nonlinear reaction-diffusion equation of Fisher-KPP type. Stability analysis explains why white bream are flourishing in the Medes Island group yet gilt head bream are struggling. One idea is to extend such a population model to a hyperbolic reaction-diffusion equation which is speed-limited, associated with a delay between overcrowding and dispersal. There is a useful class of conditionally integrable nonlinear Fisher-KPP models that reduces to the linear Helmholtz equation. The underlying nonclassical symmetry allows such a reduction for a much wider class of equations. It may be extended to solve hyperbolic reaction-diffusion equations. It may be extended to a two-species system of Lotka-Volterra type. This introduces the concept of conditionally integrable PDE, that applies also to the Madelüng quantum fluid, the Burgers fluid in 1+3D and the 1+2D nonlinear diffusion equation with D=1/u.

School of Mathematical Sciences

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