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<title>UCL Mathematics Postgraduate Seminars 2011-2012</title>

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<title>UCL > The Department of Mathematics > Post-Graduate Seminars</title>

Post-Graduate Seminars 2010-2011

UCL Department of Mathematics

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<h1>Introduction</h1>

PreSS talks (Post-graduate Research Seminar Series) re-commenced in March 2009 following their success in <a href="http://www.homepages.ucl.ac.uk/~ucahbmt/PReSS/">previous years</a>. 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 <a href="http://www.homepages.ucl.ac.uk/~ucahbmt/PReSS/">here</a>.There was also a <a href="http://www.homepages.ucl.ac.uk/~ucahbmt/mini-conference/">Post-Graduate Mini Conference</a> held in March 2008.

<h1>Upcoming Talks: 2011-2012</h1>

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

<h1 style="text-align:center">Autumn Term</h1>

Title - TBC

Nyein Chan - UCL

Friday 27th January 2012

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Title - TBC

Ali Khalid - UCL

Friday 3rd February 2012

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Title - TBC

Rob Downes - UCL

Friday 10th February 2012

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Title - TBC

Jim Oldfield - UCL

Friday 24th February 2012

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Title - TBC

Jamil Nadim - UCL

Friday 9th March 2012

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Title - TBC

Nico Laaksones - UCL

Friday 16th March 2012

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Title - TBC

Tom Ashbee- UCL

Friday 23rd March 2012

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<h1>Past Talks</h1>

<h1 style="text-align:center">Autumn Term 2011-2012</h1>

On torsion of class groups of CM tori

Chris Daw - UCL

Thursday 17th November 2011

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Title - TBC

Thomas Kecker - UCL

Thursday 24th November 2011

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Norm growth and pseudospectra for PML discretizations of open systems

Jacopo Lanzoni - UCL

Thursday 8th December 2011

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Phase transitions in a point vortex gas

Thomas Ashbee - UCL

Thursday 24th March 2011

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An unconditional proof of the Andre-Oort conjecture for Hilbert modular surfaces

Chris Daw - UCL

Friday 18th March 2011

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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.

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Mach Reflection

Mat Hunt - UCL

Tuesday 1st March 2011

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Dynamical Systems in Cosmology

Nyein Chan - UCL

Thursday 24th February 2011

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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.

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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.

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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.

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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.

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Shadow boundaries of convex bodies

Louise Jottrand - UCL

11th November 2010

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Modelling consumers

Stephen Glavin - UCL

4th November 2010

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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.

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Conceptual modelling of the El Nino Southern Oscillation

Jamie Jackson - UCL

13th May 2010

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Incorporation of frazil ice into a sea ice/ocean model

Nikhil Radia - UCL (Department of Earth Sciences)

25th March 2010

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Modelling how water droplets deform in an air stream

Hannah Fry - UCL

10th December 2009

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Dark Energy and Spinors

James Burnett - UCL

3rd December 2009

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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.

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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.

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Sudden Stratospheric Warmings

Joss Matthewman - UCL

29th October 2009

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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.

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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.

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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.

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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.

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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.

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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.

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This page was last modified on February 14, 2010 by <a href="mailto:benw@math.ucl.ac.uk">Ben Willcocks </a>

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