Department of Mathematics and Statistics Colloquium

The creation of layers within the cortex of the mammalian brain has often been of interest to researchers in developmental biology. Experiments on mice have found a counter-intuitive layering sequence. The layers are formed in an inside-out arrangement, with the deepest layers formed first and the outermost last. It is believed that the glycoprotein reelin is linked to the mechanisms behind layering. It is observed in the reeler mutant, where this glycoprotein is absent, that the layer arrangement is reversed. This has led to a number of mechanisms being proposed for how reelin may affect the neurons that form the cortical layers. No conclusive theory has of yet been established. Mathematical modelling provides an elegant method to evaluate the feasibility of different layering mechanisms. Within this talk, various models for layered structures will be discussed. Both continuum and discrete models will be discussed. After presenting the base models, I will discuss the general insights our modelling can provide for cortical layering.

For More Information:contact Guoqi Qian, email: g.qian@ms.unimelb.edu.au

Many integrable systems are characterized by the property of multidimensional consistency,i.e. the phenomenon that the relevant equation can be embedded in a higher-dimensional space-time in a consistent way.This could happen for differential equations admitting hierarchies of compatible equations, or for discrete systems on lattices which can be covariantly embedded in multidimensional discrete space-time. Recently [Lobb&Nijhoff,2009] a Lagrangian formulation was proposed for this phenomenon based on the idea of "Lagrangian multiforms". We discuss the corresponding variational principle and present several examples in 1 and 2 dimensions.

For More Information:contact Guoqi Qian, g.qian@ms.unimelb.edu.au

TBA