22/10/14 Astrostatistics: Counting extra-solar Earths, hearing the mergers of galaxies, and seeing black holes.
Dr. Will Farr (University of Birmingham)
Astronomy is entering a new era. Unlike the photographic plates of previous generations, modern astronomical data sets can comprise terabytes of databases describing the state of the telescope, properties of objects identified in the images, links to previous observations of the same field, and---of course---the actual images taken by the telescope. The vast amount of data and the special challenges of astronomical observations have given rise to a new field, astrostatistics, which is devoted to analysing these data sets and drawing conclusions about the astronomical objects in them. Through examples, including counting the number of Earth-like exoplanets in the universe, listening to the hum from merging super-massive black holes at the centres of galaxies over cosmic time, and observing gravitational waves from coalescing solar-mass black holes, I will illustrate some of the new techniques from this marriage of modern statistics---particularly computational statistics---with astronomy.
19/11/14 How to make the biggest Airbus fly
Professor Michal Kočvara (University of Birmingham)
The aircraft industry is very conservative, for obvious reasons. Usually when a manufacturer decides to design a bigger aircraft, the engineers just start with the existing design of a smaller aircraft of the same type and scale it up. However when Airbus decided to build the biggest ever passenger aircraft, the A380, this approach did not work. Using a scaled up existing design resulted in wings that were too long to fit in commercial airports. Even when redesigned and shortened, the wings were two times heavier than that which would allow the aircraft to fly. So the company decided for the first time to use "unconventional" tools of structural optimization to design their aircraft.
Structural optimization is a subject on the border between mechanical engineering and mathematics. Dealing with mechanical structures such as bridges or aircraft wings, it relies on foundations of elasticity theory. But in the search for better structures, it employs theory and tools of mathematical optimization. I will present a particular model of so-called free material optimization, in which we seek an "ultimate material", its distribution and properties. After introducing the basic mathematical formulation of the optimization problem, I will show how tools of modern mathematical optimization enable us to reformulate this model into another one, computationally much more approachable. To illustrate the practical usefulness of this technique, I will show how it was used for optimization of the leading edge of the wing in Airbus A380.
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.