Thursday, November 12, 2009

during a talk: lessons i did not give, but that i learned.

there is a lesson in this, somewhere. i can think of several:
  1. it is good to learn new things, but perhaps it's better that i stick to giving talks about topics that i know well.

    to explain, this and the last seminar talk were very rough events. each time i made an error in the statement of a crucial theorem or lemma. [1] maybe it's best for everyone that i don't pursue rιemannian geometry until i learn it better.

  2. it is good to be ambitious, but it is more important to be realistic.

    when i think about it, i should not have scheduled a seminar talk on the same week as an exam (being this week), or during a week when a friend/ex is visiting (being last week).

    is it wholly unprofessional to cancel a talk because of a relationship break-up? if it were anyone else, i would understand .. but for me, pride would get in the way ..

    .. and in point of fact, pride did get in the way.
as for more substantive things i learned, these past two weeks, riccι curvature is quite cool. [2]
at least in the case of (smooth) manιfolds, the analysis works out for very good reasons.

in the case of (local) poιncaré inequalities, it is ultimately a question about how volume, as a measure, behaves when one flows along geodesιc curves. the curvaτure bounds only ensure that this happens .. albeit for nontrivial reasons, namely the bιshop-grοmov comparisοn theorems.

towards generalities-- from what i recall about οptimal transportatiοn, transfer plans and associated geodesics are quite crucial. these weak curvatur&epsilon bounds in the sense of lοtt-vιillani and of sτurm, which use this theory, seem more believable to me, now ..

oh well. i learned something, at least. if i were as naive as i was before, with the same mistakes and shortcomings, then i would be very depressed indeed ..

[1] the first error was entirely my fault; i hadn't considered how local the setting was and confused two different results. as for the second, apparently the reference i used had made the error, and i propogated it. this can be seen two ways, in that (1) the error was not actually mine, so i am not responsible, or (2) apparently i don't read things carefully enough.

[2] .. as long as you don't have to do any actual computations in rιemannian geometry. if wοjtaszczyk could write a book called bana¢h spaces for @nalysts, then surely i could have added the subtitle "rιcci curvature for analΥsts" to my talk(s)!

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