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I audited a lecture on Topological Data Analysis, and I found it really interesting, primarily because of the connection to algebraic topology. I asked the professor if there are any connections to (theoretical) physics, and he told me that indeed there are, and that he intents to bring a cosmologist to give a relevant presentation. The professor is from the Mathematics department so he doesn't know more details. I also searched online and I could find only a few mentions about the utility of TDA in string theory and swampland.

I know the name gives it away, it's a tool for analysing data, but I would like to know if there is any utility for a theoretical physicist, for example if it offers any further intuitions, if the methods used in it are useful broadly etc. I know many string theorists have gotten into machine learning and its applications in string theory so I was wondering if it's something with similar utility.

EDIT: Now that I have seen more about the mathematical methods and tools backing topological data analysis, I feel like I could make my question a little bit more specific. Is persistence theory (persistent homology/cohomology) useful for theoretical physics? Do you know of any work using it/ or that could use it to arrive at the same result?

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    $\begingroup$ I think there's been some work applying these techniques to cosmology (e.g. this paper). I don't see how it would be very useful for string phenomenology. It's just one of many data analysis techniques. $\endgroup$
    – knzhou
    Commented Apr 25, 2022 at 21:28
  • $\begingroup$ @knzhou To be honest I haven't seen enough about string theory yet, but I know that vacuum states pose a problem. A relevant article for string theory vacua and TDA is the this. $\endgroup$
    – George Smyridis
    Commented Apr 25, 2022 at 21:39
  • $\begingroup$ Wild guess: It's useul for sorting experimental data and recreating moedls out of them $\endgroup$
    – Cathartic Encephalopathy
    Commented Apr 25, 2022 at 21:55

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