@AdrianClough Thank you for the questions. I just want to mansion that, for sheaves of p-complete spectra, many things about sheaves versus hypersheaves where done here: arxiv.org/abs/1905.06611.

@S.carmeli Thanks, I'll take a look!

Hi, first time for me here. I have a question about persistent homology and related software available to compute it, is this the right place?

definitely not

At least not this chat. I don't know about all of mathoverflow

ok, sorry for that.

@HarryGindi Why not?

I'm just saying there are no applied mathematicians in here

and PH, as it was explained to me by someone who does it, is a very applied thing

I mean, maybe I'm wrong

Well, I won't say I'm an expert, but you actually hear something about persistent homology if you hang around people doing homotopy theory

I've only heard it under the subheading of 'how can we convince people that what we do is important'

Now, I'm probably unable to answer any questions, but your answer seemed very strong -- there are definitely people working on persistent homology that are in homotopy theory research groups

Yeah, maybe

I mean, I'm not averse to Joe asking the question, but I don't think he'll find an answer here

Paris 13 had even a group de travail (topics seminar I guess?) on PH when I was there

working group

it's the same as AG in germany, I think?

Arbeitsgruppe or something

No, it's a weekly seminar on a topic

Sort of like the Prismatic cohomology seminar in Regensburg last semester

I see

maybe corresponds better to the english 'reading group'?

Hmm.. yeah that sounds about right

I guess "reading seminar" comes even closer

@HarryGindi I would suggest that as a general rule we should be as open-minded as possible about what gets discussed in the chat here. If somebody asks a question of the form "Is it okay to discuss mathematical topic X here?", the answer should (almost) never be "no". At worst, the answer should be "It seems unlikely that folks will have much to say about X, but give it a shot!".

The only marginally-plausible scenario I can think of is if somebody repeatedly asks about X with nobody taking them up on the topic of conversation. In such a case, a gentle suggestion that people don't seem particularly interested in X here might be in order.

I'd like to avoid too much "gatekeeping".

In this spirit, @joe345wa I'd say this chat is not chock-full of experts on persistent homology, but you're certainly welcome to bring it up here!

Of course, when I say we should be open-minded, I mean this in the context of mathematical discussions. I would agree that we should be a bit more choosy about what non-mathematical things we discuss.

I agree with @TimCampion

Moreover, there are very pure applications to persistent homology

@TimCampion I totally agree.

Well, I guess I was mistaken

Thanks @TimCampion my question is perhaps actually more related on the tools available rather than the PH itself, so it might still be OT. Essentially, I can see that many efficient tools for computing persistent homology and persistent diagrams exist. They usually works on point clouds and/or images. However I couldn't find a good way to get the actual clusters of a certain homology class given a filtration threshold.

Basically, given an HC, I need the clusters (i.e. sets of points) that are alive (i.e. not merged) at a certain time $t$. To my understanding this should be one of the most common use cases, and yet I couldn't find an easy way to get said clusters from the tools I've checked. I am not an expert of TDA, so I suspect that there's something in the PH that I'm completely missing. That's because to my understanding those clusters must be computed in order to create the persistence diagram.