a fleeting feeling of promise.

i can't quite put it into words, but this last conference felt different from others i've attended. i felt that, as i listened to the other attendees, i understood more than before, that my brain processed these notions more efficiently, and that occasionally i actually had something to say.

for example, a friend of mine (pekka pankka, which will soon join us in michigan) had given a wonderful presentation which derived topological consequences from function theory, and afterwards i asked a silly question about geometry ..

.. but the fact remains that i asked. it's usually someone else's inclination to ask questions; marie and kevin come easily to mind, and it was strange to hear myself ask one.

i don't know what it means. maybe it means nothing, but it remains something new.

---

a week ago i had an idea, one of many, but today it died. here is its story.

the continuing life of a summer "nomad"

in my last post i mentioned a month's travelling, but now a third of it is over:

i've returned from the bojarski conference in poland slightly time-zone-weary, glad of anglophony, appreciative of familiar american food ..

.. but best of all, not so frustrated about mathematics.

i will have many things to say about poland and perhaps i will write about them here or there, but let me first say these:

1. it was good to see old friends and colleagues from years past .. and yes, years: i've forgotten how much i've wandered since my beginnings at pittsburgh, and how many conferences i've wraithed with little known and little to say ..
   
   .. but more and more, i have more to say. perhaps they are silly or naive, but they are my ideas. i liken it to a child learning how to speak: babble comes before any wise words.
   
   i've forgotten that i remember so many people from varying places, where mathematics (specifically analysis) are spoken. we mathematicians have a culture like that of villages and tribes which to the "auslander" seems strange to see.
   
   it is even strange to me, and often so, but it is comforting. it is good to remember that you and i are not alone, when walking the path of mathematical inquiry.
   
   
2. i've forgotten how mathematics can be so varied, yet connected, but most of all, so damned interesting!
   
   perhaps it is my own disposition: i always think little of myself and what i associate with who i am, and the work and ideas of others will always merit more than mine.
   
   my best rationale is my being "a little kid trying to run with the big kids" and be warned: these older guys are pretty damned cool and brilliant and full of ideas and vigor and passion. it is infectious, and while this conference inspiration is with me, i can only be a boy, running and messing around and dreaming of great things.

endgame.

earlier today i was walking back to my office and on the way i bumped into diane and johanna. we had this very brief conversation.

diane:

"hey. how's it going?"

me:

[thinks for a moment]
"time is always against us."
[exeunt]

what i meant was:

the advisor has finally suggested an end strategy to the current project, on extensions of circle homeomorphisms. only a few computations remain, and then we return to the original thesis problem.

however, by next week he leaves for a month of holiday and i leave for a month of travelling, and if i want any completion of the matter ..

(i imagine coming back to this after a month, and forgetting intermediate subtleties, to do this over again ..)

.. then the work better be done by the end of this week. so as a result, i've been computing off and on all day. it's getting to the point where i get this loathing in my gut when i think of computing one more derivative [1] .. but the end is near, and it beckons. besides that, there are trip details to plan (i fly to warsaw this friday) and preparations to complete for when i am gone and my duties left untended.

[sighs]

i rarely think this, but a getaway vacation is beginning to sound very, very good. never mind the fact that i wouldn't know what to do with myself: the notion of intentional and uninterrupted loafing, done somewhere far away, is finally making sense to me.

[1] yes: the topic is that concrete and classical. i consistently feel as if these questions should have been answered about 50-60 years ago.

also, when i mean computing a derivative, i mean ugly implicit functions and differentiation under the integral sign. tedious, but i wouldn't call it trivial .. yet.

the limitations of work, and mind.

it's a little unlike me to be an optimist, but i feel as if i have all the pieces to settle this investigation, which concerns the "conformally natural" extension of Douady and Earle and its sobolev regularity.

so said, it's a matter of figuring out how all the pieces fit .. which isn't easy, but i think it's possible now.

i just have to trust to a little luck and work when i can. then a stroke of good fortune just might come my way.

of course, there's a problem (after all, there is always a problem):

i can't seem to work for very long anymore.

after about two hours of working i can't seem to look at the pages, at my diagrams and formulas and figures any longer. it's as if an obsession takes over; my efforts are no longer natural, but forced and artificial and meant to finish this as quickly as possible.

i grow sloppy and hurried and it makes for bad ideas and shoddy work.

usually this is not too worrisome .. hitting the mental wall, i mean.

during the academic year i never have a sufficiently large block of time to finish something as i'd like, so it never happens.

but summertime and silence are like the white of an empty page to a writer: it's condemning. there is so much space (that is, time) that you cannot stand to see all of it empty, and somehow you must fill it ..

.. and i'm at a point in my life where my hobbies and passions are few. there's sleeping and eating and coffee and the internet; every other day there's running and if my knee is up to it, saturdays are basketball. occasionally someone throws a cookout or a party and i chat a little before this newfound silence finds me again.

aside from all of that, there is silence and much nothing .. and there is work to be done. when one is not truly a person, then one can be fully committed to a cause, devoting one's mind and time .. even one's life, if the cause is worthy.

what a waste, it seems, if i can make out the goal from a distance, that i have the time, yet no able mind to see the journey through!

harmonic functions are heart-breakers.

of all the various sorts of functions that i've studied lately, harmonic functions are the ones that break my heart.

they have so many wonderful properties, including

1. they are classically (C^&infin-) smooth,
   
2. they have the mean-value property,
   
3. harmonic extensions of homeomorphisms of circles are actually homeomorphisms of discs (the Rado-Kneser-Choquet Theorem),
   

yet it seems practically impossible to discern any information about inverses of these harmonic homeomorphisms. perhaps one may say something abstractly about them, but when one tries an actual computation ..

.. forget it. they will break your heart, every single time.

i can't say it's their fault [1]. if anything, the problem seems to be an incongruency between tools in topology and in measure theory, and "natural" approaches in one area are wholly unnatural in another.

.. bah. humbug. back to work, i suppose, or at least some semblance of what work should look like.

---

[1] for the record, it also makes for inappropriate personification.