Termcard for Trinity Term 2012

Tuesday Week 1, 24th Apr – Paradoxes of Mathematical Space

Richard Earl Through the 19th century and into the 20th, mathematicians began increasingly to uncover surprises (some nice, some nasty) amongst their notions of geometry and space. Seemingly axiomatic ideas like the parallel postulate, crucial notions such dimension and volume were, all of a sudden, much less certain than had been previously been the case. This talk covers some of those seminal discoveries with a focus mainly on the Banach-Tarski paradox which states that, by means of breaking an object into finitely many pieces, its volume can be doubled; reassuringly (or perhaps not!) this is not the case with area.

Tuesday Week 2, 1st May – Members’ Papers

Various Speakers Catrin Campbell-Moore – TBC Matthew Saxton – “The Coffee Ring Effect” If you spill a drop of coffee on a surface, then the stain left when it dries is darker at the edge than in the centre. The talk will explain why this effect occurs. Annekathrin Meiburg – “Morphogen driven domain growth” Compartments are the fundamental units of size in the Drosophila wingdisc. Their size is unchanged over the large range of cell numbers which can be induced by stimulating proliferation or apoptosis. It is suggested that morphogens originating from outside the compartment regulate compartment size. However, the precise mechanism of this regulation is still largely unknown. Key to understanding the development of an organ is an explanation how a morphogen gradient changing with time and space can cause uniform, saturating growth. This talk will cover: Model organisms – why worry about the Drosophila wingdiscAn introduction to feasible models and a brief discussion of these

Wednesday Week 2, 2nd May – Blowing up a Balloon

Matthew Saxton When you try to blow up a balloon, the hardest part is near the beginning when it takes a lot of effort to make it expand more than a little. After blowing hard enough, the balloon expands quite suddenly past this stage and then the process becomes much easier. This talk will introduce the subject of Solid Mechanics (focusing on Elasticity) and use its ideas to explain why the balloon effect occurs.

Tuesday Week 3, 8th May – Fuss about Fusion

David Craven Conjugacy is a fundamental notion in mathematics, and fusion — makes non-conjugate things conjugate — has been central to modern group theory. In this talk I will take a look at conjugacy and why it is so important, discuss fusion, and give a potted history of the events surrounding its rise to the interface of algebra and topology.

Wednesday Week 3, 9th May – Fractional Calculus: differentiation and integration of non-integer order

Marcus Webb In 1695, Leibniz and L’Hôpital were discussing the newly developed differential calculus by letter. Considering the notation d^n/dx^n, L’Hôpital asked “… and what if n be 1/2?”. Leibniz replied: “It will lead to a paradox, from which one day useful consequences will be drawn.” This was the birth of the fractional calculus. The idea is to generalise the notion of differentiation and integration of order 1, 2, 3 etc. to that of fractional order s, i.e. where s is a real number. We look at the classic theory by authors such as Euler, Liouville, Riemann, and Riesz, then show how in the last 40 years real world phenomena have been modelled using the fractional calculus, confirming Leibniz’s prophecy. It is a very active research area with difficulties still unresolved.

Tuesday Week 4, 15th May – Social

None TBC

Wednesday Week 4, 16th May – Building Bombs using Quantum Mechanics

Daniel Hoek Some physicists will tell you that Quantum Mechanics (QM) is a perfectly clear, sensible and well-defined theory that has rigorous mathematical underpinnings (except for the bits that don’t). Those physicists either have no idea what they’re talking about, or they’re lying. The truth is that QM is insane, and my talk will tell the truth. I’ll go over some of the crazy experimental results that led to the formulation and acceptance of such a bonkers theory, and give a (very rough) sketch of the idiotic mathematical and conceptual framework QM uses to deal with those. We will also look at one mad application of all this: a cunning way in which the insights of QM can be used in manufacturing super-sensitive bombs. The talk will focus on the conceptual side of things and stay away from formalities: so no knowledge of physics required (and hardly any knowledge of mathematics).

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