Introduction

PreSS talks (Post-graduate Research Seminar Series) re-commenced in March 2009 following their success in previous years. The purpose of the seminar series is to inform other post-graduate students within the department about the research you are involved in. Talks are anything from 20 minutes to an hour long and should be accessible to anyone with a reasonable background in mathematics.

The seminars also provide a friendly environment for students who want to give their first talk, perhaps in preparation for speaking at national or international conferences. There is a wide range of research interests within the department and this is reflected in the breadth of topics covered in the past: we generally try to keep a good balance so that there is something for everyone. Details of past talks are given below.

Above all, these events are very informal with plenty of questions encouraged as everyone is there to discover new aspects of mathematics. Talks usually take place on Thursdays at 5.00pm

We would welcome anyone who is interested to come along whether they are a student at UCL or not. If you want further information, would like to be added to the distribution list or would like to give a talk then do get in touch with Tom Ashbee (ashbee -AT- math.ucl.ac.uk).

For talks prior to 2009, please see here.There was also a Post-Graduate Mini Conference held in March 2008.

Upcoming Talks: 2011-2012

This is a list of upcoming talks which will take place this term and may be added to in the coming weeks.

Autumn Term

On torsion of class groups of CM tori
Chris Daw - UCL
Thursday 17th November 2011

Title - TBC
Thomas Kecker - UCL
Thursday 24th November 2011

Free boundary motion, Hele-Shaw flow
Ali Khalid - UCL
Thursday 1st December 2011

Norm growth and pseudospectra for PML discretizations of open systems
Jacopo Lanzoni - UCL
Thursday 8th December 2011

Past Talks

For talks prior to 2009, please see here.There was also a Post-Graduate Mini Conference held in March 2008.

2010-2011

Phase transitions in a point vortex gas
Thomas Ashbee - UCL
Thursday 24th March 2011

An unconditional proof of the Andre-Oort conjecture for Hilbert modular surfaces
Chris Daw - UCL
Friday 18th March 2011

Talks by 1st Year Students
Pablo Bravo Soberon, Toby Davies, Rob Downes, Tom Kecker, Ali Khalid, Wenting Wang - UCL
Thursday 10th March 2011
Short talks of around 10 minutes in length by first year PhD students.

Mach Reflection
Mat Hunt - UCL
Tuesday 1st March 2011

Dynamical Systems in Cosmology
Nyein Chan - UCL
Thursday 24th February 2011

Shopping and war: applications of a spatial interaction model to complex systems
Hannah Fry/Peter Baudains- UCL
Thursday 17th February 2011
Complex systems can be extremely difficult to model due to inherent non-linearities and interactions on multiple scales. By considering the statistical nature of the system as a whole, analogies can be drawn with entropy and statistical mechanics, and progress on understanding the macro-level behaviour may be made . Using this approach, a generalised spatial interaction model is derived, yielding the most probable set of flows in a given system. We present two example applications. First, the retail model where the spatial interaction model is coupled with Lotka-Volterra dynamics to examine the flow of retail spending. Second, the war model, which considers a spatial extension to the Richardson arms race model and analyses the flow of threat between groups or armies embedded in space.

Fourier Theory - a personal journey
Jack Grahl - UCL
Friday 4th February 2011
I intend to talk about some of the themes and ideas in harmonic analysis and Fourier theory that I have come across in my research in the last few years. In the first part of my talk I will introduce the most basic constructions; the Fourier transform and Fourier series, explain their importance and talk about how they relate to what I consider to be the main themes of harmonic analysis. I will also briefly mention some of the less well-known transforms. This part will be aimed at students who do not specialise in analysis. Most of us have already come across the Fourier series and transform but I will hopefully be able to offer some perspectives and insights that you haven't encountered before. If you study analysis you might be familiar with all the mathematical facts that I go through here, but perhaps you will be amused by the subtlety of my opinions. In the second half I will give several examples of questions that I have encountered in my field of measure theory and fractal geometry, which require or suggest techniques in harmonic analysis. I intend that these will illuminate the ideas that I've introduced in the first half, and also show exactly how these ideas relate to concepts in geometry and analysis.

Towards the Shimura Correspondence
Nenna Campbell-Platt - UCL
2nd December 2010
Modular forms are functions. Their influence in Number Theory is widespread: on the one hand they have been used to answer seemingly elementary questions such as the number of ways one can write an integer n as the sum of m squares, and on the other they have formed a sophisticated piece of the proof of Fermat’s Last Theorem. The Shimura correspondence gives us a way of studying some of the harder modular forms. In this talk I’ll define one particular group, SL(2,Z[i]), and give a version of the Shimura correspondence in this case.

Decompression Model for Divers
Jean-Pierre O'Brien - UCL
18th November 2010
Ever wondered how SCUBA divers avoid 'the bends'? Bubble formation in human tissues during and after a dive can lead to serious health complications and even death. Anyone who has attended a diving course will have learnt how to plan a safe dive by not exceeding depth and time limits. However the theory that underpins even today's diving rules is over 100 years old and does not attempt to describe in much detail any aspect of human physiology or bubble behaviour. In this talk, I will discuss this classical model and highlight its limitations before examining a novel coupled bubble-tissue model developed for VR Technology that tries to more adequately simulate the decompression processes occurring in a diver's body during and after ascent.

Shadow boundaries of convex bodies
Louise Jottrand - UCL
11th November 2010

Modelling consumers
Stephen Glavin - UCL
4th November 2010

2009-2010

Equilibration of unstable baroclinic waves with and without critical layers
Ben Willcocks - UCL
10th Jun 2010
The nonlinear evolution of a single-mode baroclinic wave in the two-layer Phillips model is considered with and without Ekman friction. The behaviour of the wave is dependent on whether or not a critical layer develops. The two different types of evolution and subsequent equilibration are investigate.

Conceptual modelling of the El Nino Southern Oscillation
Jamie Jackson - UCL
13th May 2010

Incorporation of frazil ice into a sea ice/ocean model
Nikhil Radia - UCL (Department of Earth Sciences)
25th March 2010

Modelling how water droplets deform in an air stream
Hannah Fry - UCL
10th December 2009

Dark Energy and Spinors
James Burnett - UCL
3rd December 2009

The Importance of Being Discrete
Chris Taylor - University of Cambridge
26th November 2009
Scientists often want to model a system which is "discrete" and "spatially distributed": one composed of individual agents, in which information takes a finite time to travel between agents in different parts of the system. Depending on the problem, an "agent" might be a single city, a person, a single insect within the colony, a single cell within an organism, or even a single molecule.

Whilst it is theoretically possible to know what every agent is doing at one time, in order to make a predictive model we often make a continuum approximation: averaging over the discrete microstructure to form a continous macro-level model, which blurs the distinction between individual agents.

We will explore the limitations of this technique, giving examples (from sociology, biology, physics and mathematics) in which the discrete, cellular nature of the problem cannot be ignored if we want to retain an accurate description of the underlying system.

Two dimensional vortex motion near a gap in a wall
Rahul Nilawar - UCL
19th November 2009
The transport and mixing of properties of the ocean is caused, in part, by the propagation of eddies. The motion of vortices when interacting with topography such as inter-island chains and ocean ridges is modelled. The velocity field and hence the trajectories of vortices are found numerically using conformal mapping techniques and fast fourier transforms.

Sudden Stratospheric Warmings
Joss Matthewman - UCL
29th October 2009

2008-2009

Group algebras & group rings
Pouya Kamali - UCL
18th June 2009
This talk is going to be about so called group algebras or group rings. Iwill try to give two different perspectives, the first being more intuitive, and the second constructive, in the sense that we construct specific group rings from simpler building blocks. I have been using the constructive method a lot during my own research, and I will show a simple construction/deconstruction of Z[D_6], i.e. the integer group ring of the symmetry group of a regular triangle.

The effect of reconnection on the structure of a braided magnetic field
Mahboubeh Asgari - UCL
11th June 2009
I examine the effect of reconnection on the structure of a braided magnetic field. A prominent model for both heating of the solar corona and the source of small flares involves reconnection of braided magnetic flux elements. Much of this braiding is thought to occur at as yet unresolved scales, for example braiding of threads within an EUV or x-ray loop. However, some braiding may be still visible at scales accessible to TRACE or the EIS imager on Hinode. We suggest that attempts to estimate the amount of braiding at these scales must take into account the degree of coherence of the braid structure.

Convergence of random processes
Jack Grahl - UCL
22nd May 2009
This is related to work on Riemann sums and also to the pricing of financial instruments.

Local and global structure: Patching Theorems
Isidoros Strouthos - UCL
8th May 2009
Mathematical structures generally become better understood when we simplify them or move down to their constituent parts. I will try to give some examples of when this is enough to determine the overall structure, by 'patching up' the constituent parts.

Many Particle Systems
James Burnett - UCL
1st May 2009
Investigating a method to adjust the classical rate equations for particle interactions when there are finite populations of particles.

Noise propagation in a slowly varying duct
Alex Smith - UCL
20th March 2009
I will describe the essential features of sound propagation in a duct. Specifically I will be illustrating how Fourier and asymptotic analysis of the governing equations can allow the dominating physical processes to 'reveal' themselves naturally. The methods that I will be describing are elementary but nonetheless beautiful, and have applications that extend to other disciplines such as electronic engineering, banking and finance and quantum mechanics.