These seminars (unless otherwise stated) will take place on Thursdays at 1pm in Math Room 707 on an almost weekly basis.

See the map for further details. Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.

## 17 January 2019 at 12pm

**Speaker: Alexander Tetlow**

Supervisor: Dr L Oksanen

##### Title: Stable recovery of time-dependent coefficients of the Schrodinger equation

**Abstract:**

We consider the problem of determining the time- and space-dependent coefficients of the dynamic Schrödinger equation on a simple Riemannian manifold from knowledge of the Dirichlet-to-Neumann map. Based on the work of Kian and Soccorsi in the Euclidean case, we show that the electric and magnetic potentials can be Hölder-stably recovered from these data, assuming the divergence of the magnetic field is known. The talk presents joint work with Yavar Kian (Aix-Marseille University).

## 24 January 2019

**Speaker: Tibor Backhausz**

Supervisor: Prof S Zerbes

##### Title: Representation theory when p (a prime) goes to 0

**Abstract:**

The usual representation theory of finite groups over the complex numbers becomes more complicated (that is, less semi-simple) once we consider either representations of an infinite group, or a coefficient ring R replacing complex numbers, or both. The local Langlands correspondence is a surprising connection between representations appearing in different areas of representation theory that is best understood when the coefficients ring is a field, but there is also a version over (certain) coefficient rings due to Emerton and Helm. However, everything is complicated further if 1+1+...+1 (p times, where p is a prime) is zero in the coefficient ring R, and also if we want to pass from one coefficient ring to another. I will discuss analogues of the problem for more accessible examples that will hopefully give a rough idea of what I am working on.

## 31 January 2019

**Speaker: Christopher Evans**

Supervisor: Dr F Schulze

##### Title: An introduction to Lagrangian mean curvature flow

**Abstract:**

I'll introduce Lagrangian mean curvature flow in its simplest settings and try and give an idea about some of the ideas involved. The talk will be accessible to all!

## 07 February 2019

**NO SEMINAR**

## 14 February 2019

**Speaker: Sean Jamshidi**

Supervisor: Prof ER Johnson

##### Title: Vorticity competition in coastal outflows

**Abstract:**

The flow of river water into the ocean brings nutrients, sediment and pollutants from the land to the sea, and as such it is important to understand the physical processes that govern the behaviour of coastal outflows. Observations of outflows show a rich variety of behaviour due to the many nonlinear and unsteady processes at work, but in this talk I will focus on a model that isolates the effect of vorticity dynamics (essentially differences in the rotation speed of water columns). I will show that a simple integral constraint must be satisfied in order for the outflow to operate in a “coastal current mode”, and discuss what may happen when this constraint is not satisfied. I will try to explain all of the necessary ideas from fluid mechanics, so that the talk is accessible to all.

## 21 February 2019

**Speaker: Joseph MacColl**

Supervisor: Dr L Louder

##### Title: Groups in 1 and 2 Dimensions

**Abstract:**

Finitely generated groups can often be studied using topological information associated to spaces that they act on nicely; for example, the fundamental group of a space acting on the covers associated to normal subgroups. In this talk I will describe how this viewpoint helps in understanding some properties of groups and related problems I'm interested in. I will focus on the correspondences between free groups and graphs, and between groups with a single relation and 2-dimensional spaces, providing the relevant background information to make the talk accessible.

## 28 February 2019

**Speaker: Edward Goldsmith**

Supervisor: Prof G Esler

##### Title: Multi-scale methods in geophysical fluid dynamics

**Abstract:**

Multi-scale methods come in many forms, and are used across a range of applied mathematical fields. It is only relatively recently however, that meteorologists and climatologists have turned their attention towards them. This was following a £4 million investigation into the UK Met Office convection scheme, which revealed enormous holes in the methodology by which tropical convection is parameterised. Since the atmospheric waves supporting convection in the tropics can occur on much smaller scales than the finite grid on which numerical weather prediction models operate, the effects of the small-scale are only "seen" by the large-scale dynamics as spatially averaged inputs. These averages, however, do not accurately represent the phase speeds of convection-supporting waves, and thus more sophisticated techniques of parameterisation are needed.

In this talk, we will begin by looking at how the Unified Model currently treats convection, as well as outlining particular examples of where this model breaks down. We will then use a technique in multi-scale analysis called 'homogenisation' to motivate a new technique for convective parameterisation, and show that we recover more realistic phase speeds for tropical waves.

## 07 March 2019

**Speaker: Zihua (Grace) Liu**

Supervisor: Prof ER Johnson

##### Title: Oceanic internal solitary waves modeled by KdV equation.

**Abstract:**

Large amplitude, horizontally propagating internal waves are commonly observed in the coastal ocean. They are often modeled by a variable-coefficient Korteweg–de Vries equation to take account of a horizontally varying background state. Although this equation is now well-known, a term representing non-conservative effects, arising from horizontal variation in the underlying basic state density stratification and current, has often been omitted. I have examined the possible significance of this term using climatological data for several typical oceanic sites where internal waves have been observed.

## 14 March 2019

**Speaker: Holly Brannelly**

Supervisor: Dr A Macrina

##### Title: Quantile Diffusions

**Abstract:**

This research focuses on the development of a new class of continuous-time stochastic processes that allows for direct and dynamic modelling of the quantiles of data sets. These quantile diffusions are constructed by transforming each marginal of a given univariate diffusion under a composite map consisting of a distribution function and a quantile function, which in turn produces each marginal of the resulting quantile process. The transformation gives rise to the ability to alter the moments of the underlying process, for instance to introduce skewness or kurtosis to allow for more realistic modelling of data such as financial asset returns, as well as the recycling of samples of the underlying process to make simulation of the transformed quantile process easier. We derive the stochastic differential equation satisfied by the quantile diffusion, and characterise the conditions under which strong and weak solutions exist, both in the general case and for the more specific Tukey g-h, g-transform and h-transform families of quantile processes. Furthermore, a second construction of quantile processes is introduced, whereby now the parameters of a quantile function are modelled by univariate diffusions which will in turn drive the resulting quantile function-valued diffusion.

## 21 March 2019

**Speaker: Carmen Cabrera Arnau**

Supervisor: Prof SR Bishop

##### Title: SCALING OF CITIES - THE CASE STUDY OF MEDIA COVERAGE

**Abstract:**

Cities can be characterised through different urban indicators. Following an analogy with the allometric relationships exhibited by living beings, Bettencourt et al. proposed in 2007 that these urban indicators can also be predicted through universal scaling laws. We extend their work by analysing how media coverage is distributed among cities of different population sizes in ordinary circumstances. We also study the evolution of the distribution of media coverage, following an event with severe circumstances that affects a whole nation. While we observe that the amount of media coverage given to a city usually scales superlinearly with city size, this behaviour is no longer observed for some days after the occurrence of the event under consideration. Understanding how much media coverage is given after an emergency situation is important since it can have an impact, for example, on determining the amount of aid given by different governments and institutions to help with the recovery process.