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.

## 2nd November 2016

### Speaker: Ardavan Afshar

**Title: Analytic Number Theory in Function Fields**

**Abstract:**

I will begin with separate introductions to Multiplicative Number Theory and Function Fields (so you don't need to know anything beforehand) and then explain why it can be nice to ask questions from Multiplicative Number Theory in the setting of Function Fields. In particular, I will try to explore both the combinatorial perspective, which allows us to think about things like the Prime Number Theorem and Dirichlet's Divisor Problem, and the more algebraic aspect, which provides tools like Pellet's formula and helps us to understand sums of multiplicative functions.

N.B. This will be a short (and hopefully sweet) version of the talk I'll have given the previous day at the Junior Number Theory Seminar, so if you want to hear the full story, come along to that.

## 9th November 2016 in Maths Room 505

### Speaker: Hugo Castillo Sanchez

**Title: The Weissenberg number: The prince of dimensionless numbers in fluids**

**Abstract:**

"The mountains flow before the lord", proclaimed the Prophetess Deborah, who has given her name to an important non-dimensional number in rheology, the science of deformation. The basic idea is that everything will flow (even the mountains) if we wait long enough.

In this talk I will mention the historical/poetic origins of the Deborah number, which gave birth to a more important non-dimensional number: the Weissenberg number. I will show the importance of this number in the mathematical modelling of materials that exhibit memory effects. Time permitting, I will also describe how these numbers are useful to explain why some fluid-like materials (under certain conditions) might behave as elastic solids (and viceversa).

## 16 November 2016

### Speaker: Mattia Miglioranza

**Title: Mean Curvature Flow: a brief overview**

**Abstract:**

I will introduce the (most simple case of) Mean Curvature Flow (MCF) as gradient flow and as a system of partial differential equations, and, walking through the different strategies and techniques, I will illustrate some concrete examples and a main result.

## 23 November 2016

### Speaker: Kerstin Vater

**Title: An Introduction to GPU Computing with CUDA C/C++**

**Abstract:**

I'll give you a first idea of general purpose computing on graphics hardware and where it's useful. Moreover, you'll find out how to get started with the CUDA Toolkit and write your first GPU-accelerated C++ program.