Advent calendar door #22: Euromaths, Heather Harrington

We all know what data is: bits of information of which in this age of Big Data we have lots of. You might also know what topology is: the study of shapes that considers two shapes to be the same if you can deform one into the other without tearing them or gluing things together.

But what is topological data analysis? And how might it help to understand proteins or diseases such as cancer? We find out with Heather Harrington a mathematician we met at the European Congress of Mathematics (ECM) this summer. Heather tells us how topological data analysis can produce a so-called barcode for a given data set which gives deep insights into its structure. Below are a couple of images illustrating a barcode to illustrate what we talk about in the podcast.

We attended the ECM with kind support of the London Mathematical Society (LMS). Heather gave the LMS lecture at the ECM.

You might also want to listen to more episodes of our Euromaths series which reports on the ECM.

Circles drawn around 20 points in the plane. If the radius r is less than r₀, the circles are small enough to not overlap (left). Once the radius exceeds r₀, but is smaller than r₁, the circles overlap and together form a ring-like structure (middle). One the radius is larger than r₁ the circles join up in the centre of this ring-like structure. What you see now is a single blob without a hole.

The barcode captures this information. For r < r₀ there are 20 red lines indicating there are twenty connected components without holes. For r₀ < r < r₁ there is one green line indicating there is one connected component with one hole (the colours red and green differentiate between no hole and one hole). For r > r₁ there is one red line indicating there is one connected component without a hole.

Return to the advent calendar 2024!

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This content was produced with kind support from the London Mathematical Society.