The Turing Club

The Turing Club provides a programme of activities for final year MMath. and MSc. students. These activities are intended to help you think about the way in which you approach mathematics - you may find this helpful when working on your project this year. The main programme will consist of talks given by members of staff and will be centred around their own area of research and how they approach it. There will also be some talks and discussions centred around topics including research skills, careers, and recreational maths (dependent upon student interest in these).

If you have any comments/questions/suggestions please contact Dr Marianne Johnson.

Provisional Schedule, Semester 2 2016/7

Unless otherwise specified, all talks take place from 1-1:45pm on WEDNESDAYS in Frank Adams room 1, followed by tea and biscuits on the atrium bridge. (Attendees of the Turing Club talks may also like to attend the Pure Postgraduate Seminar or the Informal Applied Seminar, at 4pm on Friday afternoons.)

[Wednesday 15th February (Week 3): Postgraduate Open Day]

Wednesday 22nd February (Week 4): A Recent History of Group Theory with Prof. Peter Rowley

Much of the material in an undergraduate course on Group Theory covers results proved prior to 1900. Yet the twentieth century saw an explosion of research activity in Group Theory which continues to this day. This talk will chart some of these exciting developments.

[Wednesday 8th March MATHSOC TALK Navier-Stokes existence and smoothness - how to win $1 million with Prof. David Silvester.]

Wednesday 15th March (Week 7): The mathematics of inkjet printing with Dr Alice Thompson

Inkjet printing is a very familiar technology for graphics applications -- images are formed from separated coloured dots, printed on a page, and our brains are tricked into seeing a continuous image. However, inkjet printing can also be used as method to manufacture tiny devices and structures, such as printed circuit boards, LEDs, and scaffolds for tissue engineering. In all of these applications, printed liquid drops must coalesce in order to make a coherent structure, and this enables many interesting and unexpected interactions. In this talk, I will talk about my research on printing long thin lines from several overlapping droplets, how the behaviour can be described by quite simple models and how it might be controlled, and why experiments and numerical simulations are essential for both understanding the fundamental physical mechanisms and predicting future behaviour.

Wednesday 22nd April (Week 8): Joint models for multi-outcome data and variance structures [Rescheduled to 3rd May.]

[Friday 31st March (Week 9): Pure Mathematics Colloquium, 4pm in G.207

The algebraic theory of differential equations, Dr Omar Leon Sanchez. 

I will present the algebraic formalism of the study of PDE's initiated by Ritt and further developed by Kolchin (among many others). The main object of the talk will be the ring of differential polynomials (the analogue of the polynomial ring) a nonnoetherian ring that satisfies a Hilbert-basis type theorem. We will present classical results: Ritt-Raudenbush and Seidenberg-embedding theorems; as well as some open problems: Ritt's problem and Jacobi's bound. We will see how the recently developed theory of differential kernels can be used to check consistency of systems of PDE's and answer questions related to these long-standing problems.]

Wednesday 3rd May (Week 11): Joint models for multi-outcome data and variance structures with Dr Christiana Charalambous 

Multi-outcome data are very common in longitudinal studies, where, for example, patients suffering from a specific disease are followed up in time to monitor their progress. In this context, different types of outcomes are collected for these patients. These fall, in general, into 2 categories: longitudinal outcomes, which are routinely collected measurements (continuous or discrete) for the same patient, and event-time outcomes, which represent the time until a specific event of interest (such as death or disease recurrence) occurs for the patients. Typical research questions could be: "Is a new treatment successful in reducing the risk of patients experiencing an event?", "Are there appreciable differences between groups of patients (e.g. males vs females) in their longitudinal trajectories?" or "Is there any association between the longitudinal and survival outcomes?". In this talk, I will introduce joint models for longitudinal and survival data, which are commonly used in the analysis of such data, explain why this joint modelling approach is beneficial and also talk about my current work on extending these methods to explore possible links between multi-outcome data and variance structures.

Schedule, Semester 1 2016/7

Unless otherwise specified, all talks take place from 3-3:45pm on Fridays in Frank Adams room 1, followed by tea and biscuits on the atrium bridge. (Attendees of the Turing Club talks may also like to attend the Pure Postgraduate Seminar or the Informal Applied Seminar, at 4pm on Friday afternoons.

Wednesday 28th September (Week 1): Circular Arguments with Dr Marianne Johnson, in G.207 from 2pm-4pm.

Work as a team and try to solve as many of the puzzles as you can within the time limit. (There is a small prize for the ‘best team’, but the main purpose is to have fun talking about the problems together.)

Friday 14th October (Week 3): The mathematics of buckling with Prof. Andrew Hazel

If you have played cards, you will probably know that when you squeeze a card it bends out of plane, but why? How much force is required and what shapes can it take? Why do plastic bottles sealed at altitude crumple when returned to sea level? Why do drinking straws develop kinks when you bend them? These geometric changes are all examples of buckling, first studied mathematically by the Bernoulli's and Euler in the 18th century. Buckling can occur over a huge range of scales, from DNA to large engineering structures and has numerous applications. In this talk, I'll introduce the mathematical theory of buckling and discuss some current research problems.

Friday 21st October (Week 4): Life as an algebraist with Dr Charles Eaton

I'll talk about what it is like to do research in pure mathematics, and also a little about my own research in representation theory.

(Week 6 - PhD Open Day)

Friday 11th November (Week 7): Writing Mathematics with Dr Marianne Johnson, in G.207

I'll give some general advice on how to (and how not to!) write mathematics. Since this is best learned by experience, I will provide a couple of (very short) group exercises for you to practice with.

Friday 18th November (Week 8): Exploiting Tropical Algebra in Numerical Linear Algebra with Prof. Francoise Tisseur

Tropical mathematics is the mathematics of the real numbers, together with the operations of addition and maximum (or minimum). It has been developed for modelling discrete event systems, for solving certain  optimisation problems and as a tool for proving results in algebraic geometry.

We aim to show that tropical algebra, which is the tropical analogue of linear algebra, can also be useful in numerical linear algebra, in particular for problems with large variation in the magnitude of the elements and which are often difficult to solve numerically. We will present diverse applications of tropical algebra to matrix computations.

Week 9 TBA

Friday 2nd December (Week 10): Golfing Royally, Anciently and Tropically, Dr Mark Muldoon

The Ancient & Royal Golf Club in St. Andrews is  the governing body for golf in most of the world. They’re also industrial partners of the School’s MSc in Applied Mathematics and in this talk I will discuss work that Vinay Sudera and I did as part of his recent MSc dissertation. The problem is to model the progress of a party of golfers around the course and then explore ways to schedule tee-off times so as to simultaneously maximise the number of parties that can get around the course and minimise the amount of waiting the players have to do.

There is a modest literature in this area (and even a journal, Int. J. Golf Studies, who knew?) and I will review that, then reformulate the  problem in terms of tropical algebra - a interesting pure-mathematical structure with immediate relevance for problems involving waiting. If time permits, I'll also discuss some recent work that Gemma Lamming, a current MMath student, and I have been doing on estimating the parameters of such a model.

Friday 9th December (Week 11): Topology in Manchester since 1945: from codebreaking to symmetric squares via 2,4, and 8 dimensions, Prof. Nige Ray, in G.207

In this talk I shall try to give the flavour of living the life of a research mathematician, in particular as a topologist. The Manchester School of Mathematics has a rich topological history, and has influenced the development of the subject worldwide. The story's origins lie in 1945, and are closely related to the codebreaking work of Alan Turing at Bletchley Park. I shall outline the development of Algebraic Topology and its links with the School since then, and cite Frank Adams's famous results concerning multiplication on the unit spheres in R^2, R^4 and R^8. I hope to conclude with a brief brainteaser related to my current study of symmetric squares. 

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