Exceptional talks from lecturers at the 2018 Mathematical and Computational Sciences Showcase

24 September 2018
Dr Jeroen Schillewaert (left) with Head of Department Professor Bernd Krauskopf
Dr Jeroen Schillewaert (left) with Head of Department Professor Bernd Krauskopf

How fast can a plane on the ground turn before it becomes unstable and risks causing an accident? And what do shapes occurring in 248 dimensions look like?

Both questions were answered in stimulating talks delivered by Mathematics staff at the 2018 Mathematical and Computational Sciences Showcase for alumni, postgraduate students and friends on Saturday.

The departments of Mathematics, Computer Science and Statistics banded together to present short and lively talks on current research at the annual event, now in its fourth year. The talks were exceptional for two reasons.

Dr Jeroen Schillewaert discussed exceptional symmetries and their applications. He started by describing the non-exceptional ones, like squares and cubes, that can be seen to belong to a family. These symmetries are related to particular kinds of algebras, complex numbers and quaternions.

Complex numbers, for example, have applications in fields such as medicine and engineering, as they are ideal to describe waves. Quaternions have applications in robotics, aerospace technology and digital imaging, as they are the best way to describe rotations in three dimensions.

However, a number of symmetries are called exceptional as they don’t belong to a family. An important one is E8, which occurs in 248 dimensions and plays a central role in several theories in modern physics, such as string theory (see what the root system of E8 looks like here).

As you can imagine, the more complicated a concept becomes, the more intricate the number system needed to describe it mathematically, and the exceptional symmetries are intimately related to a very esoteric algebra, the octonions. Read a non-technical version of Jeroen’s talk here.

The other exceptional talk came from Professor Bernd Krauskopf. His discussion of the dynamics of aeroplanes on the ground is so appealing that we’ve had him deliver it for three years in a row.

On Saturday, he told the audience that planes don’t make money when they’re not flying, so airlines want to know how fast they can go on the ground. But airliners’ tricycle design isn’t made for efficiency on the tarmac.

Bernd is part of an international collaboration with European airplane manufacturer Airbus that uses dynamical systems methods to find out how fast a plane can turn before it becomes unstable. This is applied maths of a very serious kind, but there is room for fun, too.

The work has found a highly unstable turn that would see the aircraft spin out of control, skid backwards and then stop. Bernd dubs this “the Blues Brothers approach” to parking a plane. But, he says, “so far, we have been unable to convince anyone of the practicality of this.”

  • Read a story about Bernd’s work on aeroplanes here.
  • See photos from the day on the Department of Statistics Facebook page.