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:

X² - 410286423278424.Y² = 1

This quadratic equation is an example of a Pell Equation: X² - D.Y² = 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?