15 October 2014

Speaker: James Evans.

Title: An Overview of Vector Calculus.

Abstract: Vector calculus is an essential tool in most of applied mathematics and concerns itself with the differentiation and integration of vector fields mostly in 3D. The talk will build up to two key theorems; Gauss’ Divergence Theorem and Stokes’ Theorem. Applications in fluid mechanics and electromagnetic theory will be discussed.

22 October 2014

Speaker: Waleed Ali.

Title: Introduction to Statistical Mechanics.

Abstract:Ever since James Clerk Maxwell put forward the first-ever statistical law in physics, the idea of “probabilistic mechanics” became a topic of great interest for many disciplines. This seminar will merely introduce the main concepts and the revolutionary ideas that helped shape mechanics and mathematical physics as it is known today. The talk will deal with questions raised in mechanics, statistics, physics, philosophy, history and how they are all tied together. Examples of statistical mechanics will also be briefly discussed, including applications in thermodynamics, quantum mechanics and biology.

29 October 2014

Speaker: Gareth Davies.

Title: Introduction to Survey Sampling.

Abstract: Sampling theory is concerned with the problem of selecting samples that, when given a characteristic of interest, is representative of a “target’’ population. Survey sampling specifically considers sampling theory in the case where surveys or questionnaires are used to retrieve data from the sample. Various survey sampling techniques will be introduced, including simple random sampling, stratified sampling and cluster sampling. Application of these techniques in practice shall also be considered.

12 November 2014

Speaker: Xander Ramage.

Title: Introduction to Fluid Dynamics.

Abstract: The Navier-Stokes equations, which describe the motion of fluid, will be solved in some cases for which analytic solutions exist (such as flow through a pipe or channel). The Reynolds number will be introduced and its significance discussed. If time permits, the Blasius Boundary layer describing flow over a flat plate will be discussed as an example of a flow configuration without analytic solution.

19 November 2014

Speaker: Edd Lewis.

Title: On Solving Linear Systems Efficiently.

Abstract: Here we discuss the ways in which one can efficiently solve large linear systems of equations, the Ax=b problem. We will start by outlining the nature of the problem, discussing factorization techniques such as QR and Cholesky decomposition before moving on to some iterative solvers.

3 December 2014

Speaker: Brad Hardy.

Title: Introduction to Heuristic Methods.

Abstract: Heuristic methods are used when an optimal solution would require an excessive, if not infinite, amount of time to obtain. Although not guaranteeing optimality, heuristic methods find “good” solutions in much shorter periods of time. In this talk I will briefly outline why we use heuristic methods and introduce several, different approaches. Throughout, I will use the graph colouring problem (GCP) to illustrate examples and highlight my particular interest in these methods..

10 December 2014

Speaker: Stephen Moore.

Title: An Introduction to Group Theory

Abstract: Group theory has been a major area of research in pure mathematics for nearly 200 years, and has been used in a wide range of areas from Galois' proof that there is no quintic equation, to invariants for topological spaces and forming the standard model of particle physics.

The talk will introduce the basic definitions and properties of groups, then briefly cover major areas such as the classification of finite groups, group actions, representations and Lie groups.

4 February 2015

Speaker: Ross MacKenzie.

Title: Modelling large physical systems via Modelica

Abstract: The talk will give an introduction to component based modelling and the Modelica language. There will be many physical examples shown and challenges that face the approach will be highlighted.

18 February 2015

Speaker: Scott Morgan.

Title: An Introduction to Hydrodynamic Stability Theory

Abstract: Hydrodynamic stability theory aims to understand the evolution of small disturbances in fluid flows over time. An unstable flow when subjected to a small perturbation will develop into an undesirable turbulent state. Turbulence arises in many engineering applications with the most obvious being air travel. Even a small delay in laminar to turbulent transition can have major positive effects on fuel efficiency and cost.

Here we will cover basic ideas of what it means for a flow to be stable or unstable and introduce the defining equation for instability - the Orr-Sommerfeld equation. Some well-established results will be presented and some ideas about how turbulence may be delayed in practice will be discussed. Time permitting, we will briefly discuss some numerical techniques used to solve the eigenvalue problem associated with the Orr-Sommerfeld equation.

25 February 2015

Speaker: Peter Embacher.

Title: Elementary Properties of Gamma-Convergence

Abstract: Gamma-convergence is a tool particularly useful to derive meaningful limit problems in the context of calculus of variations. The goal of the talk is to introduce the basic concept of Gamma-convergence, giving the abstract definition as well as examples to illustrate the main properties and sketch the scope of applications. The most characteristic features are formulated as theorems and proved.

4 March 2015

Speaker: Jason Young.

Title: Simulating a Queue in Python

Abstract: Simulation is useful in a wide range of fields in Mathematics. This talk will give a brief overview into the algorithms behind simulations and how they can be applied specifically to a single server queueing problem. The talk will conclude with an overview of the code which will simulate a simple queue (in Python) and a quick demonstration of the software verifying theoretical results.

11 March 2015

Speaker: Matthew Lewis.

Title: Introduction to Crytography

Abstract: TBC

18 March 2015

Speaker: Alex Mackay.

Title: An introduction to Special Relativity

Abstract: What would the world look like if you were riding alongside a light beam? The simple thought experiment that lead to one of the most important advancements in human history. Einstein's revolutionary papers in 1905 unlocked a whole ocean of knowledge that we now take for granted including the famous special theory of relativity. The concept of relativity i.e. the absence of absolute motion has been understood since the days of Galileo. However this concept, when formulated by Newtonian classical mechanics clashes with other fundamental principles in physics, namely Maxwell's Theory of electromagnetism. Who was wrong: Newton or Maxwell? Einstein set out to correct the issue in his special theory, and in doing so has changed the way we perceive space and time forever.

25 March 2015

Speaker: Freddy Symons.

Title: TBC

Abstract: TBC

29 April 2015

Speaker: James Evans.

Title: What is Homogenisation?

Abstract: Abstract: Homogenisation is a theory which has been developing in a number of directions for well over four decades and captures well the behaviour of a class of problems in elasticity, electromagnetism and fluid mechanics. In this talk, I will discuss briefly the need for homogenisation methods in the analysis of partial differential equations with coefficients which depend on a small parameter. A simple illustrative example will be given to try and motivate the theory as well as an overview of the variety of problems for which this theory can be applied.