3 ms·

You may find the book "Computational Homology" by Mrozek and Kaczynski interesting (though not obviously useful). Available in the usual places. Years back I ha

You may find the book "Computational Homology" by Mrozek and Kaczynski interesting (though not obviously useful). Available in the usual places. Years back I had a chance to finish a course by the author, but being a confused physicist, I switched. Now I rediscover obvious references via HN :/

Rod 17y ago
I have just discovered Prof. Ghrist's work: http://www.math.uiuc.edu/~ghrist/index_files/research.htm http://www.math.uiuc.edu/~ghrist/index_files/research.htm I am profoundly enchanted by this stuff ;-)
- slackenerny 17y ago
  Ghrist has one nice overview article, another one comes from Gunnar Carlsson and his group at Stanford, http://comptop.stanford.edu/preprints/topologyAndData.pdf http://comptop.stanford.edu/preprints/topologyAndData.pdf (and a toy: http://www.stanford.edu/~gurjeet/mapper.html http://www.stanford.edu/~gurjeet/mapper.html), but you surely know that already. Sorry for I won't attempt to survey literature as this area is new for me too, and I don't want to confuse you, or embarass myself =) I was sure you will find these anyway. I just began dusting off my Morse theory and handful of other mathematics and I am not yet paying much attention to what present developments are directed at. One unfortnate aspect of strictly applied part of this field is that most of results and a leading conference are funded by DARPA, which leads to publications I would consider mostly recruiting material than a scientific communication. My background and goals are anyways disparate to most of the approaches so I took only cursory look.
  - Rod 17y ago
    Thanks for the info. My fields are Signal Processing and Control Theory, and I am years away from being able to contribute anything remotely interesting to this nascent field of Computational Topology. Maybe after my PhD. And, indeed, I tend to dislike DARPA-funded stuff for the same exact reasons...

Rod 17y ago

I have just discovered Prof. Ghrist's work: http://www.math.uiuc.edu/~ghrist/index_files/research.htm http://www.math.uiuc.edu/~ghrist/index_files/research.htm I am profoundly enchanted by this stuff ;-)

slackenerny 17y ago
Ghrist has one nice overview article, another one comes from Gunnar Carlsson and his group at Stanford, http://comptop.stanford.edu/preprints/topologyAndData.pdf http://comptop.stanford.edu/preprints/topologyAndData.pdf (and a toy: http://www.stanford.edu/~gurjeet/mapper.html http://www.stanford.edu/~gurjeet/mapper.html), but you surely know that already. Sorry for I won't attempt to survey literature as this area is new for me too, and I don't want to confuse you, or embarass myself =) I was sure you will find these anyway. I just began dusting off my Morse theory and handful of other mathematics and I am not yet paying much attention to what present developments are directed at. One unfortnate aspect of strictly applied part of this field is that most of results and a leading conference are funded by DARPA, which leads to publications I would consider mostly recruiting material than a scientific communication. My background and goals are anyways disparate to most of the approaches so I took only cursory look.
- Rod 17y ago
  Thanks for the info. My fields are Signal Processing and Control Theory, and I am years away from being able to contribute anything remotely interesting to this nascent field of Computational Topology. Maybe after my PhD. And, indeed, I tend to dislike DARPA-funded stuff for the same exact reasons...