Searching..
It's easy to find texts matching your various associations.. Below is an example of one such search..
What is nearly impossible is to absorb and integrate the results.. What we are really looking for (besides enriching the set of association) is a particular piece of non-trivial information, such that one is prepared to digest it and to convert it to something new..
Starting with Stefan Zohren:
http://anhinga-anhinga.livejournal.com/47720.html
One thing which attracts attention is reference 7 there:
http://arxiv.org/abs/gr-qc/0601121
and it turns out to be a very nicely written paper (worth going back to).
However, what really catches attention is the discussion of distances between manifolds on page 5 (in part, because there is always a hope for non-trivial non-reflexive generalized distance in such situation, which is something I play with these days). So I look for reference 40 and google for johan noldus. I eventually find this paper which starts with the discussion of Lipschitz distance between metric spaces, then proceeds to discuss Gromov-Hausdorff distance, etc -- all looks to be relatively simple and something I can probably use:
http://arxiv.org/abs/gr-qc/0308074
But in the process, I manage to bump into an amateur forum when people discuss Johan Noldus
http://www.physicsforums.com/archive/index.php/t-115705.html
which is interesting to read by itself, and from there up one level to the list of topics
http://www.physicsforums.com/archive/index.php/f-66.html
(what's interesting in this search is that every node is quite cool)
and here I recognize John Baez name and follow the link to a rather remarkable
http://math.ucr.edu/home/baez/week242.html
and generally try to see what might be new and interesting on his site:
http://math.ucr.edu/home/baez/README.html
He says: "I just finished running a workshop on Higher Categories and Their Applications with Eugenia Cheng and Peter May", and I remember that this was something I wanted to check out, and I go and see this:
http://www.fields.utoronto.ca/programs/scientific/06-07/homotopy/highercat/index.html
and also, while preparing this posting, this, which actually has all the abstracts (and photos):
http://math.ucr.edu/home/baez/fields/
If I would have visited this second link at that point, the story would have ended here, or would have gone in some other direction. But instead I go to Wikipedia trying to refresh my memory on "higher categories":
http://en.wikipedia.org/wiki/List_of_category_theory_topics
After a few more steps, I end up here:
http://en.wikipedia.org/wiki/N-category
and find Higher-Dimensional Categories: an illustrated guide book by Eugenia Cheng and Aaron Lauda
http://www.math.uchicago.edu/~eugenia/guidebook/
(and also, at some point, I am not sure when, a very nice list of free math books on the internet: http://us.geocities.com/alex_stef/mylist.html)
The book is cute (and now I also see that it has a tempting section "Reflexivity vs. non-reflexivity", and some tempting material on internalization). But I also look at the authors' pages and see, that Eugenia Cheng is organizing something with a remarkable name 85th Peripatetic Seminar on Sheaves and Logic:
http://math.unice.fr/~eugenia/pssl85/
The number 85 is remarkably, even shockingly big, and what's more, I am trying to find anyone in Boston who would be actively doing "Sheaves and Logic" research, and can't so far.. But this is a specific Boston problem, since I want to physically be here, and also to be able to interact on this topic without a computer at the same time..
There are probably lists of the participants of the previous meetings like this one..
If one has to select one and only one piece of information to keep from this, it would be the address of the page by Eugenia Cheng: http://math.unice.fr/~eugenia/
So this is something we know how to do these days, and something that was quite impossible even 10 years ago.. Where do we go from here?
What is nearly impossible is to absorb and integrate the results.. What we are really looking for (besides enriching the set of association) is a particular piece of non-trivial information, such that one is prepared to digest it and to convert it to something new..
Starting with Stefan Zohren:
http://anhinga-anhinga.livejournal.com/47720.html
One thing which attracts attention is reference 7 there:
http://arxiv.org/abs/gr-qc/0601121
and it turns out to be a very nicely written paper (worth going back to).
However, what really catches attention is the discussion of distances between manifolds on page 5 (in part, because there is always a hope for non-trivial non-reflexive generalized distance in such situation, which is something I play with these days). So I look for reference 40 and google for johan noldus. I eventually find this paper which starts with the discussion of Lipschitz distance between metric spaces, then proceeds to discuss Gromov-Hausdorff distance, etc -- all looks to be relatively simple and something I can probably use:
http://arxiv.org/abs/gr-qc/0308074
But in the process, I manage to bump into an amateur forum when people discuss Johan Noldus
http://www.physicsforums.com/archive/index.php/t-115705.html
which is interesting to read by itself, and from there up one level to the list of topics
http://www.physicsforums.com/archive/index.php/f-66.html
(what's interesting in this search is that every node is quite cool)
and here I recognize John Baez name and follow the link to a rather remarkable
http://math.ucr.edu/home/baez/week242.html
and generally try to see what might be new and interesting on his site:
http://math.ucr.edu/home/baez/README.html
He says: "I just finished running a workshop on Higher Categories and Their Applications with Eugenia Cheng and Peter May", and I remember that this was something I wanted to check out, and I go and see this:
http://www.fields.utoronto.ca/programs/scientific/06-07/homotopy/highercat/index.html
and also, while preparing this posting, this, which actually has all the abstracts (and photos):
http://math.ucr.edu/home/baez/fields/
If I would have visited this second link at that point, the story would have ended here, or would have gone in some other direction. But instead I go to Wikipedia trying to refresh my memory on "higher categories":
http://en.wikipedia.org/wiki/List_of_category_theory_topics
After a few more steps, I end up here:
http://en.wikipedia.org/wiki/N-category
and find Higher-Dimensional Categories: an illustrated guide book by Eugenia Cheng and Aaron Lauda
http://www.math.uchicago.edu/~eugenia/guidebook/
(and also, at some point, I am not sure when, a very nice list of free math books on the internet: http://us.geocities.com/alex_stef/mylist.html)
The book is cute (and now I also see that it has a tempting section "Reflexivity vs. non-reflexivity", and some tempting material on internalization). But I also look at the authors' pages and see, that Eugenia Cheng is organizing something with a remarkable name 85th Peripatetic Seminar on Sheaves and Logic:
http://math.unice.fr/~eugenia/pssl85/
The number 85 is remarkably, even shockingly big, and what's more, I am trying to find anyone in Boston who would be actively doing "Sheaves and Logic" research, and can't so far.. But this is a specific Boston problem, since I want to physically be here, and also to be able to interact on this topic without a computer at the same time..
There are probably lists of the participants of the previous meetings like this one..
If one has to select one and only one piece of information to keep from this, it would be the address of the page by Eugenia Cheng: http://math.unice.fr/~eugenia/
So this is something we know how to do these days, and something that was quite impossible even 10 years ago.. Where do we go from here?