a nomadic repetoire.

EDIT (AS OF 13 JAN '07): re-reading this, the list of topics sounds overly fancy and i sound arrogant. this was not my intention.

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it's strange. over the last few years i could swear that i've wandered through the hinterlands of "the quasi-world."

when i first began my thesis work, i studied Lipschitz manifolds and while doing so, for background i learned

• some differential topology, and even skimmed through that famous paper of j. milnor .. i didn't understand much of it, however, and had to read hirsch's book to understand something;
  
  
• a little harmonic function theory .. i read a little from one of the books of e.m. stein, and learned a little about fractional sobolev spaces and besov spaces;
  
  
• and a modicum about groups of hyperbolic isometries ..
  
  .. say, enough to leave a first thesis problem for dead. \:
  

and now i'm studying n. weaver's construction of measurable 1-forms and exterior differentiation. for that, i've learned about

• j. cheeger's construction of a co-tangent bundle, on doubling p-Poincaré spaces .. but only a little; i've been too lazy to read through the whole thing.
  
  
• Banach bundles and glimpsed .. nay, peeked into the world of C* algebras, which is a puzzling, cavalier mix of algebra and analysis.
  
  
• and now, i may leaf through federer's geometric measure theory, after all, for the theory of currents may be of some use to our work ..
  

i suppose that all these topics came from necessity, and i feel more "mathematically urbane" for it

but only a little; it's a little like travelling abroad for short spells. one witnesses much, acquires broader horizons, but ultimately, realises how little one knows.

.. and as for the ultimate litmus test ..

has my research come to fruition, yet?
have i written a thesis, yet?
have i proven any theorems of any relevance or worth?

the first and last questions depend on opinion, of course, but the middle one is an unambiguous no.

there is still much work to do and little time left .. and perhaps i should stop being lazy and reminiscient, stop blogging for now, and get back to work!