## Postgraduate Seminars

### Autumn 2017

These seminars (unless otherwise stated) will take place on **Thursdays at 12pm in Maths Room 706 **(25 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.

### 28 September 2017

#### Speaker: Matthew Scroggs

**Supervisor(s): Prof Erik Burman**

###### Title: The Fast Multipole Method

**Abstract:**

Over the last six months, I have been working on
implementing the fast
multipole method to speed up the computation of matrix-vector products
in Bempp: the open-source boundary element code that my supervisor and I
work on. The fast multipole method greatly decreases the time and
storage space required when working with large matrices, and was named
by SIAM as one of the top ten algorithms of the 20th century. I think it
is "quite cool".
In this seminar, I will show you what the fast multipole method is and
how we apply it to boundary element method computations.

### 05 October 2017

#### Speaker: Belgin Seymenoglu

**Supervisor(s): Dr Steve Baigent**

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

**Abstract:**

I have been
analysing a continuous-time model in Population Genetics which focuses
on two evolutionary forces at play: selection and recombination. After
plotting many phase plane diagrams for this system, I (almost) always found a
stubborn special surface in my plots, which is called an invariant manifold.
Now I have proved the manifold does indeed exist in the model for a certain
case.

You can also look forward to a helping of colourful phase plane plots!

### 12 October 2017

#### Speaker: Eleanor Doman

**Supervisor(s): Dr Nick Ovenden, Dr Rebecca Shipley, Dr James Phillips**

###### Title: Modelling the Mechanical Properties of Peripheral Nerves

**Abstract:**

Peripheral nerves
connect the brain to the rest of the human body. Any injuries to the peripheral
nerves can cause loss of permanent of function and long lasting disabilities.
The current gold standard treatment of nerve autograft currently only shows an
improvement in 40-50% of patients. The UCL Centre for Nerve Engineering is
developing new solutions to nerve repair problems. In this seminar I will talk
about my own research into what determines the
mechanical properties of nerves. I will speak about the methods such as
asymptotic homogenization that I have been using and the links to classical
solid and fluid mechanics I have used.

### 19 October 2017

#### Speaker: Desmond Xie

**Supervisor(s): Dr Johannes Ruf**

###### Title: Generalized Lyapunov function and functionally generated trading strategies

**Abstract:**We investigate
the dependence of functional portfolio generation on an extra finite
variation process. The framework of Karatzas and Ruf (2017) is used to
formulate conditions on trading strategies to be strong arbitrage relative to
the market over sufficiently large time horizons. A mollification argument and
Komlos theorem yield a general class of potential arbitrage strategies. These
theoretical results are complemented by several empirical examples using data
from the S&P 500 stocks.

### 26 October 2017

#### Speaker: Liam Escott

**Supervisor(s): Prof Helen Wilson and Dr Luca Mazzei**

###### Title: A model of particle suspensions in non-Newtonian fluid

**Abstract:**The study of particle suspensions in a weakly
viscoelastic background fluid has been a topic of research within the
non-Newtonian fluids community for around a century, and has produced some of
the most intriguing physical experiments to date. The simple process of mixing
cornflour and water comes to mind as particularly stimulating. While the
suspension I consider has an unmeasured propensity to dance on a speaker, it is
no less mathematically interesting for its complex stress equation and other
properties. In this seminar, I will convey my research over the past year,
touching on my particular cell model and the use of a tensorial structure to
find analytic solutions for flow quantities in an otherwise barren stretch of
numerical approximations.

### 02 November 2017

#### Speaker: Mihai Nechita

**Supervisor(s): Prof Erik Burman andDr Lauri Oksanen**

###### Title: Finite element methods for ill-posed problems. Unique continuation for the Helmholtz equation

**Abstract:**A well-posed problem has a unique solution that
depends continuously on the
data. The design of finite element methods (FEM)
for PDEs usually relies on the well-posedness of the continuous
problem. But not all problems are well-posed.
I will show how some ill-posed problems can be numerically solved using
stabilized FEM, with particular focus on results that E. Burman, L.
Oksanen and I have recently obtained for the unique continuation problem for
the Helmholtz equation.

### 09 November 2017

#### Speaker: Alex Doak

**Supervisor(s): Prof Jean-Marc Vanden-Broeck**

###### Title: Travelling wave solutions on a ferrofluid jet

**Abstract:**It has been known since the work of Lord Rayleigh that a
capillary dominated jet is unstable to long wave perturbations. This
instability (known as the Rayleigh-Plateau instability) is why exposed streams
of fluid tend to break into droplets. It is found that magnetic fields, when
applied to a ferrofluid in the correct way, can stabilize this instability. In
this talk, I will discuss this problem, and present stable traveling wave
solutions. I will focus in particular on what the dispersion curve can tell us
about what kinds of solutions to expect in the problem.

### 16 November 2017

#### Speaker: Antigoni Kleanthous

**Supervisor(s): Dr Timo Betcke, Dr David Hewett, Dr Anthony Baran **

###### Title: Calderón preconditioning for electromagnetic scattering of dielectric objects

**Abstract:**In recent years Calderón preconditioning and appropriate use
of basis functions has become a popular strategy to speed up the iterative
solution of electromagnetic scattering problems. In this talk I will discuss
how to use the boundary element method to solve dielectric scattering problems,
how the properties of Calderón projectors can be used to apply the Calderón
preconditioning and demonstrate its implementation in the boundary element
library BEM++. I will then extend the theory to electromagnetic scattering by
multiple dielectric objects and present results for light scattering by ice
crystals.

### 23 November 2017

#### Speaker: Márton Mester

**Supervisor(s): Prof Gavin Esler**

###### Title: The polar vortex and the Kida-model in a slowly changing stochastic background flow

**Abstract:****In the winter
stratosphere, temperature difference between the equator and pole leads to a
low-temperature, low-pressure area at high latitudes, the so called
stratospheric polar vortex. While about twice in three years on average the
Northern Hemisphere vortex is destroyed by planetary wave activity, the
Antarctic vortex has experienced such an event only once since we have
observations. When the vortex experiences this dramatic change, it is
either displaced off the pole or split into two subvortices. In either case,
cold patches of polar air detach and bring colder, snowier winter to
midlatitudes. On the other hand, the lack of these events on the Southern
Hemisphere is linked to the Antarctic ozone hole. **

The aim of the talk is to introduce a relatively simple model of the polar vortex evolution under suitable conditions and explain how it may predict vortex split events.

### 30 November 2017

#### Speaker: Nikoleta Kalaydzhieva

**Supervisor(s): Prof Andrew Granville**

###### Title: Continued Fraction and Pell’s Equation over Function Fields

**Abstract:**In a letter to Eratosthenes, Archimedes, posed the so-called
cattle problem, asking for the number of bulls and cows that belong to the Sun
God, subject to some arithmetic restrictions. This problem boils down to
solving the following quadratic equation:

*X*^{2} - 410286423278424.*Y*^{2} = 1

This
quadratic equation is an example of a Pell Equation: *X*^{2} - D.*Y*^{2} = 1, where D is an integer.
This version of Pell and its connection to the continued fraction of √D is very well understood.
The question that we will be interested in is what can be said when we take X,
Y and D to be polynomials. Do the same results hold?

### 07 December 2017

#### Speaker: Various

###### Title: 5 Minute Christmas Talks

**Abstract:TBC**