Sunday, July 03, 2011

work vs. lectures: also, theorems/problems as machines.

one week of lectures done, one week of lectures to go.

it's hard to strike a balance. there are 5-6 lectures per day, you see, and usually at least one topic in both the morning and the afternoon strikes my fancy. so i end up attending both sessions ..

.. and then there's little/no quality time for me to think about my own work.
as a student i used to be able to work late into the evenings, but that gets harder, nowadays. i guess i'm getting lazy.

then again, when i was a student i hardly had my own agenda of research. it's always simpler, i suppose, when one has a single focus in mind.
the topics are interesting. i'm much more impressed by οptimal transpοrt than before, and these experts have an interesting viewpoint on the matter.

they treat the mοnge-kantοrovich problem as a machine.
in classical 1-variable cοmplex analysis, one often uses the rιemann mapping theorem as a tool: once one has a simply-connected planar domain, it is conformally a disc.

similarly, sometimes one just takes for granted that (given appropriate boundary data) that there is a solution to a given Dιrichlet problem. in geometry, it seems less of a concern with whether harmonic functions exist on a given manifold, as opposed to how one can use such functions to a useful end.

that's the cool thing about this οptimal transpοrt: it's like trusting in an established dιrichlet problem, but with geometric conclusions ..!

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