The mathematics of algebraic topology has many unexpected applications. It is well designed to solve problems that have a geometric flavour but where the geometry is flexible rather than rigid. One example is the coverage problem for sensor networks. Given a team of miniature robots with limited sensing capabilities, we wish to distribute them over a region. How can we be sure that we have covered the entire region, using as few measurements as possible? It turns out that algebraic topology has a neat answer to this question. Everything can be done using the methods of undergraduate linear algebra, carefully organised to describe the geometric scenario. This is joint work from around 2005, with co-authors Robert Ghrist and Abubakr Muhammad.
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