Hydrocephalus is a serious medical condition which causes an excess of cerebrospinal fluid (CSF) to build up within the brain. A common treatment for congenital hydrocephalus is to implant a permanent drainage shunt, removing excess CSF to the stomach where it can be safely cleared. However, this treatment carries the risk of vascular brain tissues such as the Choroid Plexus (CP) being dragged into the shunt during drainage, causing it to block, and also preventing the shunt from being easily replaced. In this talk I present results from our fluid-structure interaction model which simulates the deflection of the CP during the operation of the hydrocephalus shunt. We seek to improve the shunt component by optimising the geometry with respect to CP deflection.

We describe a network model for the progression of Alzheimer's disease based on the underlying relationship to toxic proteins. From human patient data we construct a network of a typical brain, and simulate the concentration and build-up of toxic proteins, as well as the clearance, using reaction--diffusion equations. Our results suggest clearance plays an important role in delaying the onset of Alzheimer's disease, and provide a theoretical framework for the growing body of clinical results.

Holography, which reveals a specific correspondence between gravitational and quantum theories, is an ongoing area of research that has known a lot of interest these past decades. The duality of holography has many applications: it provides an interpretation for black hole entropy in terms of microstates, it helps our understanding of solid state properties such as superconductivity and strongly coupled quantum systems, and it even offers insight into the mysterious realm of quantum gravity. 

In this talk, I will first introduce the concept of holography and some of its applications. I will then discuss some notions of string theory and geometry that are commonly used in holography. Finally, if time permits, I will present some of our latest results, where we match the energy of membranes in supergravity to properties of the dual quantum models.