overall it's been a good visit, but intense and tiring. i've tried to do a good job with the lectures, but not at the expense of research.
.. which would explain the suboptimal planning of my lectures!
as of now, my colleagues and i have gotten headway into a well-defined project, maybe two. there are still many details to consider, but we've thought long enough and hard enough on a few problems that i believe something can be done with them.
one part makes me cringe, though: i might have to revisit some of the basics of some slightly arcane topics in functional analysis ..
.. such as the weak-star operator topology ..! [1] 7-:
to be fair, i think that it's been easier on me than on them. often i do most of the listening and little of the talking. it went the other way around, this time.
[1] to be precise, the wiki directs to the weak operator topology, not the weak-star operator topology .. but on the other hand, what i would call the weak-star operator topology differs from what the corresponding wiki would suggest; i claim that one doesn't actually need the underlying source and target spaces to be the same .. much less hilbert spaces .. \-:
one part makes me cringe, though: i might have to revisit some of the basics of some slightly arcane topics in functional analysis ..
.. such as the weak-star operator topology ..! [1] 7-:
to be fair, i think that it's been easier on me than on them. often i do most of the listening and little of the talking. it went the other way around, this time.
over the last two weeks i felt like i explained a lot about a theory that nobody seems to study very much .. which is a shame, since i've consistently found it a rather useful theory. by sheer exposure and effort, i think i've also convinced my collaborators of the same.for my own part, i learned quite a bit about fractals .. and in some sense, fubini's theorem, too.
so i did end up being useful, in some fashion .. which is relieving. in spain these days, research funds aren't easy to come by. imagine if they had invited me and gotten little out of the deal! (-:
[1] to be precise, the wiki directs to the weak operator topology, not the weak-star operator topology .. but on the other hand, what i would call the weak-star operator topology differs from what the corresponding wiki would suggest; i claim that one doesn't actually need the underlying source and target spaces to be the same .. much less hilbert spaces .. \-:
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