George. Abstract: A partition of a positive integer is a way of writing it as a sum of positive integers. I will present some simple examples and results which stem from this definition, building up to the (not so simple) Rogers-Ramanujan identities. Chris will provide cacke afterwards in the common room.
Elena. Abstract: I have prepared a three course menu that we will use as an excuse to understand from a scientific point of view some of the things that happen in a kitchen. This will include life demonstrations and of course a little bit of tasting. Cake will follow as usual in the common room, courtesy of Daniele.
Nairn. Abstract: The constant pi has been known about for many millenia and is used in almost all branches of mathematics. Indeed, mathematicians have always been fascinated with evaluating this constant numerically: from fractional approximations, to series expansions of increasing practical use. In my talk, I shall give a brief overview of pi's evaluation and then shall demonstrate an algorithm that is simple to derive but converges very rapidly.
Hugh. Abstract: Last summer I finished writing up my thesis, and the plan is to talk through the results presented there, hopefully in a very accessible way. So come along, see my first presentation as a doctor, and learn how to write a thesis. Also, we'll play some toric geometry bingo.
Eric will rigorously define the Wiener Process, the probabilistic model for Brownian Motion, while providing some intuition as to why such a model is suitable. he will then show the existence of such a model due to the construction first introduced by Lévy. Cake afterwards courtesy of Stuart.
Julia Collins will discuss the fascinating history of the man who invented the word 'mathematics' and who turned it into a way of life. Who was he? What did he believe in? Why didn't he eat beans? What did he think the universe sounded like? And did he ever prove the famous theorem that is named after him? Musical accompaniment will be provided by Andrew Wilson. Togas optional.
Daniele Sepe. Over the complex numbers we have a canonical form for matrices, called the Jordan normal form. Over the rationals we also have a canonical form for matrices, called the rational normal form. A natural question to ask is whether this still holds over the integers. In this talk we will see how asking this question is tantamount to understanding some of the structure of algebraic number fields. Very little knowledge of abstract algebra will be assumed and there may even be some surprising results!
Giacomo Mazzi. Abstract: I will present the idea of Model Reduction for dynamical systems, and in particular a method we developed. I will apply this method to a toy system showing what are the results and possible upgrades. Cake provided by Stuart this week.
Dr. Richard Archibald will give a brief history of video games with an emphasis on the increasing relevance of mathematics and physics as hardware improves in performance. This talk will contain chat relating to the graphics library OpenGL but this should not deter people from coming as it will actually be discussed and is not the usual codeword meaning that the talk will be cancelled at the last minute ;-). As much of the material as possible will demonstrated using video and live running code.
Mathieu Carette will tell us about "Groups generated by reflections". There will be drinks and nibbles afterwards, then we will go on to a pub.
There will be 2 guest speakers. Andrew Stothers will tell us about "Email management or the art of pressing the delete button" and Achim Nonnenmacher in person will talk about "The life and achivements of Achim Nonnenmacher". It will be followed by the School's Cheese and Wine reception on the 3rd floor at 7pm.
Stuart Murray will tell us about the algorithms used in image compression. Often simple ideas from mathematics, information theory and even psychology can provide tools for compression. The talk will be a brief tour (with examples) of some of these methods, with particular focus on that most ubiquitous of image formats - JPEG. Hopefully you'll never again wonder what happens in the split-second after saving using the .jpg extension!
Graeme Taylor will show (non-mathematically) how the public key approach to cryptography allows for a secret to be established over an insecure channel. He will then explain the discrete logarithm problem in group theory, which is the basis of modern implementations such as elliptic curve cryptography.
David Urminsky will give us an overview of chaos theory with some simple examples, then go on to look at the driving forces behind chaos in the solar system. In particular, he will look at the dynamics of the asteroids between Mars and Jupiter.
Pamela Docherty will tell us about the various imaging techniques with which we can study the structure and functions of the human brain. She will introduce one in particular, Magnetoencephalography (MEG) and discuss the inverse problem associated with it.
Hugh Griffiths will investigate the effect of puzzles on mathematicians. If there is time, he will also look into the effect of mathematicians on puzzles. There will be lots of toys to play with!
