Term 3
Wednesday 17th May (Harrison 250)
Huda Mahdi
Mathematical modelling of whole brain activity.
Here we provide a mathematical analysis of a well-established mathematical model of whole brain activity (electroencephalogram or EEG) in a cortical column and event related potentials (ERPs), which was developed by Jansen and Rit (1995). The model comprises three interacting neural populations represented by three nonlinear second order differential equations, respectively. Our aim is to analyse computationally the model's behaviour applying dynamical systems and bifurcation theory. We investigate how the behaviour of the system changes as the model’s parameters change, with a particular focus on the influence of the amplitude parameter of the excitation populations and the parameter representing the input to the system.
Wednesday 31st May (Harrison 250)
Mark Heavey
Picard groups of affinoid p-adic spaces (slides)
Affinoid spaces are an analogue of complex analytic spaces, and to a lesser extent, smooth manifolds for non-archimedean fields such as the p-adic numbers. A powerful tool in number theory and algebraic geometry, the theory closely mimics the theory of classical varieties in algebraic geometry. As well as introducing the above topics, in this talk we will consider the Picard group of such spaces, and show that under certain arithmetic conditions such groups are finitely generated. There is also a more-scheme theoretic approach based on formal schemes which we will touch briefly upon.
Wednesday 7th June (Laver LT3) 15:30-16:30
Ned Williams
The El Niño-Southern Oscillation as a Source of Climate Predictability (slides)
Prediction of the weather is heavily dependent on the initial conditions of the atmosphere, whereas projection of future climate relies on the boundary conditions which force the entire system. Climate prediction, on the other hand, is useful at intermediate timescales and largely concerns the boundary forcing of the troposphere, which itself relies on the initial conditions of other components of the climate system, such as the ocean, cryosphere and stratosphere. A dominant mode of interannual climate variability is the El Niño-Southern Oscillation (ENSO), which is an irregular fluctuation of sea surface temperatures in the Tropical Pacific. In this talk, I will introduce ENSO and how it impacts climate across the globe through teleconnections. I will then demonstrate how increased ocean resolution in HighResMIP models impacts the simulation of ENSO and its important teleconnection to the North Pacific. We find that the spatial pattern of warm El Niño and cool La Niña events is greatly improved with increased resolution, and the asymmetry between the two phases improves but remains underestimated. The spatial pattern and amplitude of the El Niño teleconnection improves, but the La Niña teleconnection weakens; we attribute this undesired effect to mean state precipitation biases.
Thursday 29th June (Harrison 250)
Madhuparna Das
A brief overview of the Hardy-Littlewood Circle Method. (slides)
We talk about the Hardy-Littewood circle method and its application to the Waring problem. Further, we introduce the saddle-point method which can be considered as a coarse version of the circle method. Finally, we explore its application to the Waring-Goldbach-type problem.