## Postgraduate Seminars

### Spring 2017

These seminars (unless otherwise stated) will take place on **Thursdays at 5pm in Christopher Ingold G21 Ramsay Lecture Theatre **** **(Christopher Ingold building, 20 Gordon Street) 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. They are generally followed by tea and biscuits in the Mathematics Department Staff Room (Room 606, 25 Gordon Street) - see how to find us for further details.

### 9 February 2017

###### Speaker: Alex Doak

**Title: A finite difference scheme applied to long finger-like bubbles (but not Saffman Taylor fingers!)**

Abstract:

If one takes a long tube filled with water, and then quickly releases the bottom part of the container, after initial instability, a stable finger of air rises at constant speed through the water. It is found in experiments that for large values of the Weber number (this means that surface tension is not very important compared to gravity or inertial forces, and will be explained in the talk), the speed and shape of the bubble is given uniquely by the radius of the tube. However, one finds that when solving this problem mathematically with surface tension T=0, an infinite set of possible solutions is found for a given tube radius. This degeneracy can be solved by including surface tension in the model, and taking T --> 0. This singular limit T-->0 has 'selected' a solution out of an infinite set, and furthermore, the given solution agrees very well with experiments. The profiles and nature of these solutions will be discussed. Since the problem is heavily non-linear, the approach is primarily numerical.

### 16 February 2017

###### Speaker: David Hodgson

**Title: Assessing the cost-effectiveness of potential vaccination strategies against Respiratory Syncytial Virus**

Abstract:

Respiratory Syncytial Virus (or RSV) is the most important pathogen in causing acute lower respiratory infections in infants, which is the leading cause of childhood morbidity globally. With vaccines against the virus on the horizon, it is of interest to public health policy decision makers whether the health benefit acquired from vaccinating against RSV is worth the added healthcare cost. This talk will discuss the mathematical methods that can be implemented to answer these questions, including an introduction into how to to build transmission models of infectious diseases and also how to calibrate such models using adaptive Metropolis Hasting algorithms.

### 23 February 2017

###### Speaker: Pietro Servini

**Title: Helen, before we knew her**

Abstract:

Theseus slayed the minotaur and fled Crete to take his place, through misfortune, as king of Athens. In time, his path crossed with that of Helen of Sparta, daughter of Zeus, later Helen of Troy. And thus she was separated from her home for the first time…

The consequences of flow separation in aerodynamics are usually to be avoided. In this talk, we’ll see why it happens and what its effects are, before moving on to study the separation of the boundary layer for flow over a bump. But who, exactly, will be our Dioskouroi?

### 2 March 2017

###### Speaker: Bernhard Pfirsch

**Title: Formulas of Szegő type - a motivation from quantum physics**

Abstract:

Within the last 60 years mathematicians like G. Szegő and H. Widom extensively studied truncated Toeplitz matrices and their continuous analogue truncated Wiener Hopf operators. In particular, they proved asymptotic determinant formulas respectively trace formulas for such operators as the truncation parameter tends to infinity. As this might all be Greek to you I will try to give a motivation from quantum physics for the study of these operators. The aim is then to explain the mathematical results in a physics context.

### 9 March 2017

###### Speaker: Jason Vittis

**Title: Minimal epimorphisms and the R(2)-problem**

Abstract:

In 1956 Eilenberg first investigated minimal epimorphisms and minimal resolutions. We will explore a generalisation of Eilenberg’s idea and see how it applies to the R(2)-problem.

### 23 March 2017

###### Speaker: Belgin Seymenoğlu

**Title: Invariant manifolds of a model from population genetics**

Abstract:

In 1976, Nagylaki and Crow proposed a continuous-time model for the population frequencies, which focuses on one gene with two variants (or alleles). Much of my time has been spent plotting phase plane diagrams for this model, but whatever values I put in for the parameters, I always find a stubborn special curve in my diagram - an invariant manifold. I proved that the manifold does indeed exist in the model for a certain case and, more recently, relaxed the conditions so there is no need to assume the system is competitive. If time permits, I will also display a gallery of my colourful phase plane plots showing that the invariant manifold need not be unique, smooth or convex.