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Feb, 2020
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Topology and Engineering

Talking about topology and engineering, I remember Raoul Bott studied engineering when he was a student. His thesis at Carnegie Mellon University is entitled “Electrical Network Theory”.

And now, Robert Ghrist. He is very actively trying to apply mathematics, including algebraic topology, to problems in engineering. A lot of papers and expositions can be downloaeded from his website. For example, he wrote an article [ dSG07b ] on his work on sensor networks.

I had a chance to listen to Ghrist’s talk during the conference on braids in Singapore in 2007. His talk and presentation techniques are impressive. Furthermore, he said that he is advertising algebraic topology to peaple in engineering, since algebraic topology is useful.

Applications of algebraic topology discovered by Ghrist and his collaborators include the following.

In their study of sensor networks, a classical way of constructing a simplicial complex from a covering, called the Rips complex, used by Vietoris in 1920’s is used.

Daniel Cohen and Pruidze [ CP ] refer to [ Lat91 Sha97 ] for motion planning.

Adler and his collaborators [ ABB + ] used persistent homology .

It is interesting that they used the phrase “applied algebraic topology” in their paper. It seems the topics in this page are forming a new research area.