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These seminars (unless otherwise stated) will take place on Thursdays at 5pm in Room 500 the Mathematics Department on an (almost) weekly basis - see how to find us for further details. Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students. They are generally followed by tea and biscuits in the Mathematics Department Staff Room (Room 606, 25 Gordon Street).
30th April 2015
Title: The Banach-Tarski Paradox
The Banach—Tarski paradox says that it is possible to cut up a ball, and reassemble the pieces into two copies of the original ball. This is one of the most famous “paradoxes” in maths, because it is easy to state but very counterintuitive. I will give an accessible proof (no post-first-year maths will be required) that you will be able to repeat in the pub to your fascinated friends whenever the subject comes up.
Wednesday 6th May 2015 in Room D103
Title: Hyperbolic Lattice Point Problems
Starting with a brief history of the topic, we will see how different counting problems have a natural interpretation coming not only from the obvious geometric setup, but from an arithmetic point of view as well. In the hyperbolic space there are many complications introduced by the odd geometry and an excess of eigenvalues, for example. We will see how this relates to the heat and wave flow on our manifold and, in particular, how this impacts the problem in different dimensions.
14th May 2015
Title: Time travel in general relativity
I will discuss the possibility of general relativity allowing time travel. I will talk about various solutions that allow closed time like curves, such as wormholes. I will then consider various paradoxes that this leads to, and possible ways of resolving them.
21st May 2015
Title: ... And Icarus Flew
In Greek mythology, Icarus - son of the master craftsman Daedalus - on wings made of feather and wax, flew too close to the sun: the wax melted and Icarus fell into the Icarian Sea, where he drowned. In this talk, I will introduce some of the main concepts of flight and chart humankind’s discovery of them; discoveries that have allowed us to go from developing more aerodynamic spears to inventing vehicles that fly hundreds of times faster than Icarus could ever fly and sending spacecraft distances greater than Icarus ever thought existed.
28th May 2015
Rafael Prieto Curiel
Title: The mathematics of policing
Research concerning social issues, like crime, is a multidisciplinary task that requires Social Scientists, Urban Planners, Engineers, Statisticians and without a doubt, Mathematicians. There are broad types of models that have been used for criminal issues, and some make use of great parts of the spectrum of Applied Mathematical tools, like spatial models, pattern recognition methods, network analysis, time series, complexity and agent based models, partial diﬀerential equations and dynamical systems.
Crime can be analysed from the perspective of the criminal, the victim, the place where it occurred and can focus on the reasons why it happened or the impact that it has. However, research should not stop there and should be focused on how to use the many results obtained through the many models to improve our society, either by doing prevention, prediction, reaction or analysis of the crime. For that reason, a key component has to be the work of the police forces.
Questions like how many police oﬃcers are needed and where to allocate them will be tackled during the presentation. Real data from Mexico City will be used and presented to show the extreme relevance and the impact of a good mathematical model in improving our social well-being.
4th June 2015
Title: Numerically Solving PDEs with Finite and Boundary Element Methods
Many real life situations give rise to Partial Differential Equations (PDEs) which cannot be solved analytically. In these cases, fast numerical methods are needed to allow computers to find the solutions to a high degree of accuracy. Two popular methods within science and engineering are the Finite Element Method (FEM) and the Boundary Element Method (BEM).
11th June 2015
18th June 2015