bad day.

the advisor is away, again.
life goes on, and so does the thesis work.

in the last few days i've had occasion to look through parts of that tome, h. federer's geometric measure theory. the idea is to recast the problem at hand in the language of currents, and by determining what type of current it is ..

(say .. rectifiable or normal, or a flat/polyhedral chain)

.. we may gain some leverage in identifying necessary conditions for a space arising from n. weaver's construction.

well, that was the idea.

i can't seem to find that leverage .. or any leverage, for that matter. the theory of currents is tricky in its geometry and my formulation doesn't fit very clearly or well, in it.

two days ago, i pondered flat m-chains and how to detect them .. specifically, whether a particular current (induced by the weaver construction) is a flat chain. i think i may know my answer, bit i'm unsure if it helps to know.

if it is correct, then there's little need to bother with the theory of currents; the burden of the problem will remain in standard measure theory.

perhaps i just have to improve my formulation of the problem. i don't know .. and i hate not knowing.

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anyways, today was a paranoid day. i was mired in examples, non-examples, and pathologies, and it made for a foul mood.

strangely enough, my spirits improved a little, after i went on a short run through the UM arboretum .. in 20-degree weather, of all things ..

.. but only a little. having spent little time at the office this weekend, even spending the evening hours there took some adjustment of habit. i think i was surly and dismissive in my encounters around the department, today.

east hall is boisterous and chaotic. i never seem to think very well when there, with undergrads underfoot and fellow math grads excitedly interruptive and distractingly diligent.

tomorrow is another day, perhaps a better day. i'm not one for optimism, but there seem few viable alternatives. should i expect worse tomorrow and dull my efforts, amidst great sighs of "alas?"

of course not. i have a problem to solve .. or at least, to kill.

when one thesis problem dies, it's hard not to think that the next one could die, too.