What do you think about the new, exiting connections between QFT, Homotopy Theory and pattern recognition, proof verification and (maybe) AI systems? In view of the background of this forum's participants (selfreported in the survey mentioned a few days ago), I guess most of you follow those developments with some attention.
Concerning Homotopy Theory, there is a coming [special year](http://www.math.ias.edu/node/2610), you probably know Voevodsky's [recent intro lecture](http://www.channels.com/episodes/show/10793638/Vladimir-Voevodsky-Formal-Languages-partial-algebraic-theories-and-homotopy-category-), and [this](http://video.ias.edu/voevodsky-80th) even more popular one. Somewhat related are Y.I. Manin's remarks on the missing quotient structures (analogue to localized categories) in data structures and some of the ideas in Gromov's [essay](http://www.ihes.fr/~gromov/PDF/ergobrain.pdf).
Concerning ideas from QFT, [here](http://arxiv.org/abs/0904.4921) an example. I wonder what else concepts come from it?
BTW,... (read more)
That is hard to estimate, but I think I need the same or less time for studying them. But of course the issue is how one reads them and how much one spends into extracting the hidden ideas and translating them into one's own mental structures (instead of turning one's mind into an emulation of the author's one) . One can study and understand very advanced papers fast and well without a productive "translation", and the more one knows, the easier it is to restrict reading that way.