Queen Mary Mathematics Research Centre

QUIPS Seminar

(Queen Mary Internal Postgraduate Seminar)

Programme for 2008

All talks are on Wednesday at 12pm in room 513 (Maths). Refreshments will be provided after the talks. Everyone is welcome.

Winter Term

Date	Speaker	Title
8 Oct 2008	E. R. Vaughan	Vizing's Theorem and Related Topics
15 Oct 2008	No talk
22 Oct 2008	John Faben	On the Complexity of Counting Modulo k
29 Oct 2008	Johanna Rämö	Octonions
12 Nov 2008	Derek Patterson	The Cone Condition and Generalised t-Designs
19 Nov 2008	No talk
26 Nov 2008	Adeel Farooq	Coxeter generators for the baby monster
3 Dec 2008	Victor Falgas-Ravry	Roth's theorem via discrete Fourier analysis
10 Dec 2008	Colin Reid	From finite to profinite

Previous talks this year

Date	Speaker	Title
1 Feb 2008	Andrew Curtis	Tie Hard: An Introduction to the Mathematics of Neckties
8 Feb 2008	Johanna Rämö	Solving the Rubik's cube
15 Feb 2008	Sally Gatward	An introduction to Λ-trees
22 Feb 2008	John Faben	An introduction to complexity theory: P and NP
29 Feb 2008	No talk (leap year holiday)
7 Mar 2008	Saiful Islam	Bayesian sample size determination using loss function plus cost function
14 Mar 2008	Ben Parker	Who wants to be a statistician?

Previous seasons of QUIPS: 2007, 2006, the rest.

Andrew Curtis. Tie Hard - An Introduction to the mathematics of neckties.

This talk will be based on the work of two Cambridge mathematicians, Fink and Mao. They noticed that despite the myriad possibilities for different tie knots only four were in general usage. Rather than rely on trial and error to come up with new designs, they decided to use the power of mathematics to characterise and categorise all the possible knots. By making certain restrictions to exclude those which were aesthetically unappealing they were able to produce a further nine possibilities. The talk will involve a brief exposition of their methods and results. Neckties will be supplied for those of you wishing to try out some of the more recherche designs. Bruce Willis will not be appearing. (For more details see the poster.)

Johanna Rämö. Solving the Rubik's cube.

You will learn how to solve the Rubik's Cube. The algorithm uses basic group theory, and I will be talking about permutations, quotient groups, commutators and conjugation. But you do not need to know anything about group theory to be able to learn the algorithm. If you have a Rubik's Cube, bring it with you.

Ben Parker. Who wants to be a statistician?

Your chance to win huge prizes as we play “Who Wants to be a Statistician?”. Can you see your way through the media myths that are repeated every day in the press? Are 87.6% of statistics made up? Does it matter? Can good statistics actually be useful? This game requires very little mathematical background at all, so please come and play!

(Any resemblance to any other game shows entirely coincidental)

Victor Falgas-Ravry. Roth's theorem via discrete Fourier analysis

Szemerédi's celebrated theorem states that any subset of the natural numbers with positive upper density contains arbitrarily long arithmetic progressions. Diverse proofs for this fact have been found, ranging from the purely combinatorial proof of Szemerédi (1975) to the ergodic-theoretical proof of Furstenberg (1977). More recently, Gowers (2001) found a novel approach to the theorem using a mixture of discrete Fourier analysis and combinatorics.

In this talk, I will run over the basics of discrete Fourier analysis and, following Gowers, prove a weak form of Roth's theorem (Szemerédi's theorem for arithmetic progressions of length 3) before describing further applications and refinements of the techniques thus developed. Essentially no prior knowledge of Fourier analysis or number theory will be assumed.