Dr. Peter Eccles lectures for The Galois Group - Wednesday 3rd December 08

Dear All,

You are invited to attend the next Galois Group lecture, which will be given by Dr. Peter Eccles on Wednesday 3rd December 2008 at 1:10-2pm in the Alan Turing Building (room G.205). Please see the abstract below and do recall that registration is not required - you just have to turn up! Free refreshments are also available at the end.

For further information or any queries please feel free to contact Dr. M.D Coleman or myself.

Best wishes, Galimatias (!)

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Wednesday 3rd December 2008 at 1:10-2pm
Alan Turing Building, room G.205

Peter Eccles

Abstract - From Perspective to the Projective Plane

During the fifteenth century artists made significant advances in the use of perspective in order to give an impression of depth in their pictures. Leon Battista Alberti wrote the first text on this subject in 1435. I will describe his method for drawing a square tiled pavement and illustrate it using a photograph of the Alan Turing Building taken by Nick Higham.

Alberti's work led to questions about what geometrical features different views of the same object might have in common. The answer to this question was provided by Girard Desargues in 1639 with the introduction of projective geometry. In this, additional 'points at infinity' are added to the Euclidean plane so that any pair of straight lines in the plane meet at a unique point (which is a point at infinity if the lines are parallel). This feature is observed when viewing straight railway lines going into the distance: they appear to meet at a point at infinity. I will give an example of how Desargues was able to unify certain disparate results in Euclidean geometry, by observing that they are all special cases of a single result in projective geometry.

In more modern times, topologists have studied the projective plane as a single object in its own right. In 1902, Werner Boy constructed a model of the projective plane in three dimensional Euclidean space. I will describe one method for constructing this model. I will also mention some unsolved problems relating to models of this type.

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Two Student Lectures by The Galois Group

Dear All,

The Galois Group returns with another set of general audience lectures, but on this occasion you will be presented with two lectures given by undergraduate students. Please show support to your fellow classmates and attend on Wednesday 12th November at 1:10-2pm in room G.207 (Alan Turing Building, The University of Manchester).

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Wednesday 12th November 2008 at 1:10-2pm
Alan Turing Building, room G.207


Pete Green - Bootstrapping - Not just securing your footwear!
Abstract:
Ever needed more data than you were able to collect? Ever needed to solidify some statistics or create confidence intervals with a small sample size? Then bootstrapping your sample could be a very useful solution!

Third-Year student Pete Green gives a basic introduction to this simple, but powerful Monte Carlo sampling method, along with some real-life applications and worked examples!

And

Kristjan Korjus - Building a machine that makes money!
Abstract
Kristjan is going to talk about a machine that beats the stock market! He will try to explain the concept of financial modelling and also touch on topics such as money, ethics of financial markets, genetical algorithms and MatLab.

There will be discussion of the theory behind making this machine along with some of the issues he encountered while working on the project.

In the end you should get some interesting ideas about money and our society with recommended articles for further reading.

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The lectures are open to anyone, and registration is not required. Please do come along, for apart from an interesting lecture you will also have some refreshments to chomp on afterwards!

For further information or any queries please feel free to contact Dr. M.D Coleman or myself.

See you all there!

First Galois Group lecture of the semester - Categorification

Professor Nige Ray, a name known to all, especially to first year undergraduate students at The University of Manchester (UoM), kindly agreed to give the first Galois Group lecture of the year. The Galois Group is an undergraduate Mathematics society* at the UoM, who aim to organise regular general audience lectures throughout the year, given by staff and undergraduate students.

The lecture was titled Categorification, a word which spell check refuses to correct, and one which I had trouble pronouncing myself when introducing Professor Ray! What's categorification? you ask. Well perhaps Professor Ray's abstract (below) might give you a brief idea, but this does not mean that I do not remember his lecture (although it was on Wednesday 13th October 2008 - some time ago, I hope you will agree!).

"Thousands of years ago, when people were learning to count their sheep (amongst other things!) the process of decategorification was seen as a stroke of genius, that allowed the development of number. During the last 30 years, it has dawned on mathematicians and theoretical physicists that the time has come to reverse this process, and work through ideas that had never been properly developed beforehand, but which are just as fundamental to mathematics as counting. In its own language, categorification involves replacing sets with categories, functions with functors, and equations with natural isomorphisms. I shall try to make some sense of this for a general mathematical audience."


In the build up to the lecture you could say that I had been surprisingly optimistic, namely due to the large room that I had booked in the Alan Turing building for the lecture. I wasn't to be disappointed (surprisingly!) as a record number of 89 people - ranging from undergraduate students, staff and some guests - attended a fantastic and interactive lecture. The one thing that stands out from these lectures is the atmosphere throughout the event. It was electric. I left the building for a second and observed the audience, which reminded me of why I enjoy organising these events. Everyone seemed to be in a different world altogether - that of categorification and counting sheep!

There exists a group of students (half of our audience!) who want to attend such lectures, and now they have the opportunity to do so. This year I have been trying to advertise the lectures in other universities around Manchester, and at the refreshments after the lecture (during which only one Jaffa Cake survived!) I was pleasantly surprised to find a retired IMA member there, who asked to be added to the mailing list for future lectures. The refreshments are as important as the lectures in my opinion, for they give students the chance to interact with staff and other mathematicians too, and you can always interrogate the speaker on something you didn't understand!

Such lectures are also a brilliant way of giving someone a snippet of a certain topic in maths. Now categorification is a blessed topic which has something for everyone (well there was mention of finite sets, abelian groups, vector spaces, knots etc), but if after the lecture you don't find it appetising then that's perfectly okay. The lectures are windows into areas of mathematics that one might not have the luxury of studying.

Whoops I digress! (I'm afraid you'll have to get used to this!). Overall the first lecture of the semester was a success, and I would like to thank all those who attended and I look forward to seeing you all at the next student lectures (which will be advertised in due course).

*Note: more than one society exists. We cater for the mathematical community whereas mathsoc caters for the "social aspects" of University life.