**Very** interesting interview with an applied topologist. Just as John Cook (the interviewer) I had no idea applied topology was a thing. Would not have thought homology can help with planning cellular network coverage. Apparently it does.

johndcook.com/blog/2010/09/13/

@herid - my friend and former student Nina Otter is one of many people working on applied topology; she's using persistent homology in climate science. Her paper "A topological perspective on weather regimes" is open-access:

link.springer.com/article/10.1

I went to a big conference on Applied Topology in Japan a while ago; it seems to mostly be persistent homology.

A topological perspective on weather regimes - Climate Dynamics

It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as ‘weather regimes’, loosely categorised as regions of phase space with above-average density and/or extended persistence. Their existence and behaviour has been extensively studied in meteorology and climate science, due to their potential for drastically simplifying the complex and chaotic mid-latitude dynamics. Several well-known, simple non-linear dynamical systems have been used as toy-models of the atmosphere in order to understand and exemplify such regime behaviour. Nevertheless, no agreed-upon and clear-cut definition of a ‘regime’ exists in the literature, and unambiguously detecting their existence in the atmospheric circulation is stymied by the high dimensionality of the system. We argue here for an approach which equates the existence of regimes in a dynamical system with the existence of non-trivial topological structure of the system’s attractor. We show using persistent homology, an algorithmic tool in topological data analysis, that this approach is computationally tractable, practically informative, and identifies the relevant regime structure across a range of examples.

link.springer.com
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@johncarlosbaez Very interesting. Climate science would have been behind even cellular network coverage on the list of things where I thought homology might be of use. nonwithstanding the fact that when I teach the hairy ball theorem I also always give a formulation that there is always a place on Earth with no wind.

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