## How weird is your shape?

Topological science and technology

Topological science and technology

* Click image to enlarge.

Topology is a field of study in which a doughnut is equal to a tea cup! You see they both have only one hole in them. If you imagine they are made of wet clay then you can deform one into the other. Topology originated as a branch of mathematics and has played an important role in the development of physical theories, for example in Einstein’s general theory of relativity.

We use Topology at our Graduate School to understand materials, networks, economics, and computers from a broader perspective.

Weird crystals: a Möbius strip can be made by turning a strip of paper by 180 degrees before sticking the ends together. Who would have believed that a crystal could form in this shape? This was achieved for the first time in our Graduate School.

Now we are now measuring the properties of such crystals to find new uses for them.

Optical and acoustic vortices: everyone knows that water will form a whirlpool when it goes down the plug hole. What about whirlpools of light or sound? We are busy visualizing them. The centre of the whirlpool is a special point that is called a singularity. Water, sound and light can show these.

Topological defects: soft matter like soap or liquid crystals can have very surprising properties. If you try to organize liquid crystals by applying an electric field, for example, their molecules do not always line up as you might expect; instead defects spontaneously form. We are studying such topological defects with the aim to elucidate analogies with different fields of topological science.