3/12/14 The Mathematics of Voting
Dr. Chris Good (University of Birmingham)
We tend to feel fairly smug, living in democracies, about our system of government, but are elections fair? Do they really reflect the views of the electorate? Certainly many people are unhappy with the ‘First-Past-the-Post’ electoral system used in the UK, espousing instead some form (or other) of proportional representation. Would such a system be better? How can we make a judgment?
In fact, when we analyze voting mathematically, it becomes clear that all system of aggregating preferences(electing a parliament or a president, agreeing on who should win Pop Idol or Strictly Come Dancing, deciding the winner of the Premiership or the Formula 1 Championship) can throw up anomalies, unfairnesses and down-right weirdness.
How weird can things get? Well, in 1972, Kenneth Arrow (Harvard, USA) and John R. Hicks (Oxford, UK) were jointly awarded the Nobel Prize for Economics ‘for their pioneering contributions to general economic equilibrium theory and welfare theory.’ At the heart of Arrow’s contribution to economic theory is his so-called ‘Impossibility Theorem,’ which (roughly speaking) says that there is no fair voting system. More precisely, once we agree what a fair voting system is, one can show that the only fair voting system is one in which there is a dictator who decides what every outcome will be. But there clearly cannot be a dictator in any fair voting system, so a fair voting system is impossible.
In this talk, we shall compare some voting methods and then discuss Arrow’s Impossibility Theorem. Hopefully the talk will engender surprise, contention and disbelief.
21/1/15 Fighting disease with mathematics
Dr. Sara Jabbari (University of Birmingham)
How can mathematics be used to understand antibiotic resistance, track the dynamics of viral infections or even develop new drugs to tackle disease?
As our knowledge of diseases becomes increasingly detailed and complex, more tools are required to interpret and use this information. Mathematical modelling is one such tool. Differential equations can be employed to simulate and understand disease mechanisms, venturing into places that experimental work cannot go, be that for practical, financial or even moral reasons.
We will explore a range of examples illustrating how maths can be used to understand disease, improve existing treatments and create entirely new ones.
18/2/15 The real science behind Parallel Universes
Dr. Tony Padilla (University of Nottingham)
Have you always wanted to be a rock star? In a parallel reality your wish came true. Is this the real life, or is this just fantasy? Learn about the real science behind parallel universes as I take us on a journey of discovery through the multiverse to different parallel worlds, from those that exist all around us to those that are unimaginably far away. Travel across the landscape of string theory to watch new universes bubbling into existence, and visit island universes that are marooned in a sea of extra dimensions. Understand how you can create new universes closer to home just by tossing a coin, and find out why you might be nothing more than a Boltzmann brain, floating through empty space with false memories.
18/3/15 Mathematical Lego: building a model plant
Dr. Rosemary Dyson (University of Birmingham)
It may not always seem like it, but plants can undergo incredible shape changes and movement, from leaves following the sun through the course of a day, to the Venus flytrap catching its prey, to trees growing over 100m tall. If we want to understand, and hence control, these shape changes (for example to make a crop grow better under drought or flood conditions) we need to understand how a single cell can manipulate the mechanical properties of its cell wall, what those properties tell us how an individual cell grows, and what that in turn tells us about how lots of cells tightly stuck together (i.e. the whole plant) behave. This is where mathematical modelling comes in!
Using equations which describe how the bits of the cell wall interact as the building blocks of our mathematical models, we can use maths to work out what the overall behaviour will be. It is a bit like using small individual Lego bricks to build a much larger physical model. This lets us see what effect making changes to individual cells has on the shape of the whole plant. In turn, this allows us to find out lots of interesting things about how plants work, but much more quickly and cheaply than with traditional biological experiments! This work has transformed the way we study plant growth, and now forms the basis of research undertaken around the world.