Pure Postgraduate Seminars

The Pure Postgraduate Seminar Series provides an informal environment for pure maths postgrads to present mathematical ideas. If you would like to give a talk or have any comments or suggestions as to the organisation of the seminars please contact Simon Baker or David Naughton. Every week, a reminder will be sent to all Pure Postgrads. If you are not a pure postgrad and would also like to be sent a reminder then please e-mail us.

The seminars are held in the Alan Turing Building, Frank Adams Room 2 (1.212), Fridays from 4pm to 5pm. We will have tea, coffee and biscuits before the seminar at 3:45pm on the Atrium bridge. In the evening, we often go to a pub.

For the Autumn 2011 seminar timetable, please click here.

Spring Semester 2012

20^th Jan 2012
An overview of Ergodic theory
Simon Baker

Abstract (click to view)

Ergodic theory can be described as the statistical and qualitative behaviour of a given system that evolves with time. In this talk I shall give an overview of several key topics arising from this field. We shall see applications to Number Theory and Fractal Geometry (there will be pictures).
27^th Jan 2012
An introduction to o-minimal fields
Javier Utreras

Abstract (click to view)

During the 80s, van den Dries, Pillay and Steinhorn introduced the concept of o-minimality, which allows to reproduce nice properties of semialgebraic sets in extensions of real closed fields. In this talk, I shall define o-minimality and give an overview of some of these properties.
3^rd Feb 2012
Poisson Geometry (+ Deformation Quantization)
Adam Biggs

Abstract (click to view)

Poisson geometry is the arena in which mathematicians tackle questions pertaining to the study of dynamicals systems that have similar properties to the standard flat Hamiltonian method. We shall describe what such objects are and lightly explore the mechanics that can be defined on them, mainly through examples. If we have time we shall also define what a deformation of a Poisson algebra and try to explain the philosophy behind this form of quantization. Again this will be example heavy to try and get a feel of what is going on.
10^th Feb 2012
An Introduction to Complex Dynamics
Dave Naughton

Abstract (click to view)

I wanted to call this talk 'Why those pictures look so full on awesome' but I decided to be sensible. Don't worry it won't happen again. So, we've all been asked the question by friends and family pretending to be interested - 'so what is it you do your PhD in?' - if maths doesn't scare them off, pure maths likely will. If they stick around long enough to hear 'Ergodic Theory and Dynamical Systems' then they look at me like I've got 10 heads (however...). So when asked what is it you do I usually just mention fractals and the Mandelbrot set. Even the bloke who sells pies down Wigan market has probably seen Th'Mandelbrot Set somewhere down the line. Or maybe not. Anyway i'm going off on a tangent once again. In this talk my main aim is to introduce complex dynamics and Julia sets. These arise from iterations of seemingly simple polynomials with complex coefficients, but the results can be very interesting. I want to talk about how these things are constructed, and why they look like they do in all the computer generated fractal images we see on many mathematics books. I will also relate this to an application of Newton's Method for finding zero's of polynomials, in particular how the choice of a starting point in the Newton iteration determines which (if any) root the method will converge to, and how this leads to fractals. Then I'll talk about the construction and properties of the Mandelbrot Set itself, which is intrinsically related to Julia Sets. There will be plenty pictures, hopefully not too many definitions and it should be pretty straightforward and accessible to all. The only prerequisite is a knowledge of what a complex number is - so yeah, everyone should get something from it, even the pie bloke from Wigan market, but unfortunately he takes his Whippets out for a walk on a Friday afternoon. Also more tangents are inevitable.
17^th Feb 2012
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Sian Fryer

Abstract (click to view)

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24^th Feb 2012
Title
Rafael Alcaraz Barrera

Abstract (click to view)

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2^nd Mar 2012
Title
Amit Kuber

Abstract (click to view)

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9^th Mar 2012
Title
Laura Phillips

Abstract (click to view)

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16^th Mar 2012
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Alastair Darby

Abstract (click to view)

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For the Autumn 2011 seminar timetable, please click here.

Previous Seminars

List of 2010/2011 seminars (Philip Bridge)
List of 2009/2010 seminars (Richard Harland)
List of 2008/2009 seminars (Ali Everett)
List of 2007/2008 seminars (Jacob George)
List of 2006/2007 seminars (Stephen Clegg)
List of 2005/2006 seminars (Marianne Johnson)
List of 2004/2005 seminars (Matt Horsham)
List of 2003 seminars (Matthew Craven/Sara Santos)
List of 2002 seminars (Sarah Perkins/Sara Santos)