## Postgraduate Seminars

### Autumn 2016

Christopher Ingold G21 Ramsay Lecture Theatre

These seminars (unless otherwise stated) will take place on **Wednesdays 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.

### 12th October 2016

###### Speaker: Belgin Seymenoglu

**Title: Invariant manifolds of another model from Population Genetics**

Abstract:

Not long after my last seminar, I moved on to analysing another model in Population Genetics. This one looks at two evolutionary forces: selection and recombination. After plotting many phase plane diagrams for this system, I (almost) always found a stubborn special surface in my diagram, which is called an invariant manifold. I set out to prove that this manifold exists in the phase plot, only to accidentally show that a second manifold turns up when the fitnesses satisfy a certain condition(!) You can also look forward to a gallery of colourful phase plots showing these two manifolds!

### 19th October 2016

###### Speaker: Rudolf Kohulak

**Title: Freeze-Drying, Stefan Problems and Level Set Methods**

Abstract:

Freeze-drying is a process widely used in the pharmaceutical industry as a simple solution on how to reduce the water content of temperature sensitive materials and increase their stability and shelf life. However, at the moment freeze-drying remains the most expensive stage of pharmaceutical manufacturing, and hence further modelling is needed. To model the process we consider Stefan Problems. A Stefan Problem is a particular boundary value problem that arises in modelling heat transfer with phase change (water freezing, ice melting...). Hence the challenge is to capture the progression of the interface separating different phases of the material. We conclude the talk by considering different numerical methods for solving the model; in particular we focus on the level set method.