This workshop focuses on two specific areas of Topological Design: the topology of networks; and topological optimisation. Topology refers to the properties of objects which remain unchanged when stretched, twisted, crumpled, or bent without tearing, gluing, or closing holes. For example, did you know a coffee mug is a doughnut? If you had a rubber-like material, could you show this? We intend to explore these complex ideas via two engaging practical activities: 

1. The first activity challenges students to organise themselves into groups, forming connections based on specified rules, and 

2. The second activity challenges students to produce the lightest cardboard bridge possible - while sustaining the weight of a toy car - by only cutting material away, instead of adding it. 

The first introduces the students to the topology of networks by exploring flow from one person to the next generated by certain rules, while the second places them in the position of a topological optimiser as they manually undergo the process behind the mathematical tool known as topological optimisation. 

To accompany these activities we give small presentations related to our research as PhD students to illustrate the significance of topology in varying scientific disciplines as well as demonstrate that a PhD is an achievable goal to aspire to in the future. 

This activity is a response to our favourite FAQ: "What does topology have to do with the real world?". With just a few strips of paper, some double sided tape, and a pair of scissors, we're able to replicate the mechanism that DNA uses to unzip itself and show how the topology of the DNA affects what shape it will form after splitting in half. So how does it work?

First students cut a few long strips out of a sheet of paper. With the first two strips, they tape them into a simple loop - like a bracelet - and with the remaining two strips, into a Möbius band - essentially just a loop with a twist in it (see image on left).

By taping together different combinations of these loops and then cutting the loops down the middle, we can simulate chains of DNA breaking apart. Each unique combination of Möbius bands and simple loops stuck together yields surprisingly varied results when split in two, but we won't spoil the fun!