my "day off"

after submitting my thesis, i tried to enjoy myself. i browsed through a bookstore, but that only lasted a little. i tried to sit at a cafe and read a book, but i couldn't commit to it.

it was hard to let maths go. so i didn't.

---

i did a few mathematical things, none of them too hard. i fiddled around with latex and with my thesis files.

without the rackham thesis template format,
my thesis shrinks from 145 pages to 107.

i'd call that progress. q:

after thinking it through, i wrote back an answer to a mathematical question i received via email about one of my conference talks.

and so it went.


today i woke up, had a cup of coffee, and played around with an idea in efforts to prove a conjecture. i still don't know if it works, but not because i've found a flaw in the logic.

rather, i should say that i have a bad feeling about it. there is a way to decompose null sets in euclidean space -- due to @lberti, c$ornyei, and prei$$ [1] -- and i'm extrapolating from their results.

the idea makes sense, but i can't visualise it geometrically. i have a hard time imagining an explicit nontrivial example. this should <<ping>> on anyone's mathematical radar.

i wouldn't be surprised if the idea is silly and doesn't add any effective structure. one way or the other, i just want to know.

i also leafed through a friend's doctoral thesis.

i must say, it's nice to read maths that's been written clearly and deliberately, like a thesis, that is NOT my own.

this is not to say that i spent the whole day working: hardly that. it's just a difficult transition to stop doing maths altogether.

yesterday i went wall-climbing and went out to the pub with friends.

today i went bike-riding and grocery shopping, and i cooked dinner for myself -- a proper dinner -- for the first time in ages. it wasn't a bad dish, either.

[1] laugh all you want, but this blog should NOT come up as one of the first hits for the reference that i am .. er, referencing. consider it an active vigilance.

endgame.

now, the job is done.

rather, one job is done;
i've kept one promise, and there are a few more to keep.

but this was the most important one.

---

i went to rackham graduate school [1] today with an unbound copy of my thesis, and i met with a friendly woman who walked me through the formatting.

there were no rulers.

there was no transparent sheet to put over pages,
in order to check specifications, such as margin lengths (to the millimeter).

there was nothing of the sort,
no draconian measures taken,
nothing to weed out graduates unmindful of the rules and regulations.

..then again..

i had to rename a chapter or two, because their titles said "appendix" and the graduate school couldn't have that .. but that was all.

no complaints here.

when it was all done, the woman who helped me gave me a official certificate, that i have "hereby completed all requirements towards a Ph.D at the U of M" or something like that.

amazingly enough, they spelled my name correctly.
there was even a shiny gold University seal on it.

so i guess i am a doctor now.
it still doesn't seem real.

i had thought that the toil of editing and re-editing and more re-editing of the thesis manuscript would sink in the idea.

by the time i submitted my thesis, i would feel that i deserved it, for all that this year and years have put me through.

well, no. it still doesn't seem real.
can i be really Dr. _____?

no matter, that;
titles are of little importance, anyway.

---

when i woke up this morning, i thought a little about what would happen if this actually worked out [2]. nothing came to mind, and it worried me.

when this is done, will i have a purpose?

when you've spent every waking day, either working or worrying,
pushing yourself to finish "one last thing" ..

.. which becomes a half-dozen things,
and takes an hour longer than you'd have liked ..

.. when you fret inwardly,
even when you see your friends at conferences,
itching to go back to work because you feel you must ..

when it is all done, what then?

before my meeting, i received an email. someone's asking about my Ann Arbor talk. someone wants to know a few more details.

someone actually cares?!?

so for now, i have a question to answer and an email to write. come to think of it, there are a few other questions to think about ..

.. a few more promises to keep.

i don't know why, but unconsciously i thought that my world would collapse, once the matter of a thesis was settled. i can deal with disasters -- i call it "graduate school" -- but successes and endgames ..

.. i never plan for those.


at any rate, there's work to do and i want to do it;
more to come, about that.

[1] though i am/was a graduate student in the mathematics department, there is a single graduate school for the entire U of M, called the Horace H. Rackham School of Graduate Studies.

[2] this morning and the night before, i mostly thought of contigency plans B, C, and D, in case the rackham people felt that something was wrong with my thesis formatting.

for the record, plan B was to rescale the printout margins, plan C was to remove all footnotes (which were unnecessary but slightly informative) for new versions of plan A and B, and plan D was to figure out how much summer tuition cost, if it came to that.

thoughts of holiday, some mathematical.

i made a list of plans, after i submit this thesis. here are some of the mathematically-related items.

0. take a few days off, maybe a week;
(but that doesn't really count as something "to do," per se)

3. think casually about a research problem that my sister told me;
(mathematical sister, not biological)

4. read the mathematical work of my peers,
and the work of those i wish to follow.

---

i should elaborate on the last item and some sentiments i've recently expressed. first of all, i'm not sick of mathematics. in fact, after these last two conferences, there are some ideas that i'm really excited about ..

.. well, excited insofar as i have moments to really ponder them. the thesis is still heavy on my mind ..

but i am just sick of my own thesis. it would be nice to look at some mathematics that i didn't write (read: ruin with my gaffes and bad habits).

this is probably excessive to say, but i need to stop my own work for a while and remember why mathematics is worth pursuing.

in my own works, all i see are my errors and my shortcomings. there is some good in those results, but i cannot appreciate them now.

---

it's been a long year.

next fall term i'll begin a new life in a not-so-new but very cool place. if i've noted anything lately, "new" may mean 'good,' but it often means 'complicated.'

so i suspect that the forthcoming years will be good, but also long. it will be a new journey. maybe this is a good time to take a short rest, and remember why i chose to take that journey ..

.. after all, i'd rather not be complaining, every step of the way!



** on an unrelated note: this is post #401 on this blog. i guess it's been that long since i've begun.

countdown.

two more days. that's what i tell myself.
two more days before the thesis submission deadline for U of M.

two more days before my meeting with the graduate school administrators, in order to pore over the words and margins and font sizes.


by then, i can give up on my thesis,
and i can say: "good enough!"


until then, there are two more days to go. argh.
how does everyone else make this look so easy?

a letter by any other name .. seems strange to me.

currently i'm revising one proof which is about 4 thesis pages long [1] and i keep running out of indices. fortunately the indices are not nested -- no sub-sequences or sub-nets or anything like that -- but they serve different purposes:

• i is for the ith coordinate in euclidean n-space;
  
• j is an index for sets in a cover;
  
• k is a positive integer, which grows arbitrarily large;
  
• l is for another euclidean coordinate.
  

i just realised that i used k twice, and i'm not sure if i used m yet ..

.. minor annoyances. it could be worse.

it is interesting, though, how we associate some letters to specific mathematical roles.

m and n always seem like integers to me,
p and q exponents for the lebesgue spaces,
r for radii of metric balls,
s and t are continuous parameters or variables,
u and v are unit vectors,
w and z are complex-valued variables,
and we all know x and y.

.. anyways, back to work.

[1] when reformatted, it probably converts to 2 1/2, possibly 3 pages in the standard amsart package.

a first casualty of the thesis war edit: never mind on second thought ..

in efforts to expedite thesis editing and rewriting, i elected to remove all discussion of one particular theorem from my thesis.

as for why:

1. the theorem doesn't have any implications towards other facts in my thesis. it's expendable.
   
   
2. a revision of my initial "proof" will be a rigorous proof, but the details are too many to do in one weekend, when coupled with all the other things i have to fix.
   
   on a bizarre but related note, smooth functions are overrated.
   
   
3. it's not my theorem anyway, and i've been told a good proof of it already.
   
   i had wanted to give my own proof because i couldn't find one in the published literature. it's not as good as the one i was told. however, since i was proving facts with similar tools anyway, it wouldn't have hurt.
   

in light of constraints of time, it's not worth keeping the proof i have in mind. it would have been nice -- to relate my work with the work of another mathematician -- but it's not like i lost a theorem or anything.


if anyone's curious, it's Theorem 3.3 in "Curr3nt$ in M3tric $p@ces" by Ambr0si0 and Kirchh3im. [1]


if you want to know the proof -- and are willing to read the finished version of my thesis -- then email me, and i'll write you something about it.

---

so we have one recorded casualty. i fear there may be more.

if worse comes to worse, there is one chapter that can be completely eliminated from the thesis. i had written it to motivate and to relate my theory to an existing theory ..

.. but if i have to choose between edited correctness and relevance, maybe this time i will choose edited correctness.


EDIT (@ 14:39): i spoke too soon. it's an easy fix, so i think the proof can go back in nicely. however, in order to see it, you will still have to read my whole thesis. sorry! q:


EDIT (friday @ 12:14): i re-spoke too soon. the details are more gory than i thought, and it remains not worth writing. if you want to know about it, email me.



[1] no, those aren't expletives. the title and names are obscured. among you, the experts know the authors whom i mean. i'm tired of this blog arising from google searches from which it shouldn't arise.

well, it's over.

i stand by what i said before:

      "i like the math in this talk;
      it's a good story."

i just wish that it was someone else who tells the story of the schoenflies problem and its various incarnations.

i love telling stories, but i'm no good at storytelling.

---

as you can imagine, the usual process happened:

1. days before, i am excited about giving a talk and the mathematics involved. i think of how cool the theorems are.
   
   
2. the day of the talk, i'm nervous and worried that something is amiss, that it's all wrong, and that i'll forget to say subtleties that matter to me.
   
   indeed, i will forget to say them. i always do.
   
   
3. after the talk, i realise that i've forgotten again: i hate giving talks. it never goes as well as i would like.

oh well. at least my friend (who talked at the same time, in a parallel session) won most of the audience. truth be told, i wanted to hear what he would say.

sometimes talks do get in the way of a conference .. \:

a little about "mathematical" family

in the last week or so, it has been good to see members of my mathematical family [1]. there were some "sibs" of mine that i had encountered but never met, others whom i rarely see or write, and others with whom i see all the time.

today, both of my younger sibs -- they are still students [2] -- gave talks, and i think they were well-received. they also spoke last week, at the advisor's memorial conference, and i think they now stand well in the mathematical world.

viewing it, i would call it something like a debutante ball -- that is, a coming of age, a proper introduction into our mathematical society.

they will go far. they might deny or be uncertain about it, but from an outsider's viewpoint -- it's obvious. perhaps it is good for them to worry a little, but they needn't do so.


i've never been very good as a brother -- biological or mathematical -- but it makes me happy to see this. it's been a hard year for anyone who knew the advisor -- we lost him -- and in the event of this tragedy, it's heartening to see these sibs of mine flourish and thrive.

call it familial pride.


[1] the analogy of advisor and student as parent and child will never disappear. the mathematics genealogy project is a testament to this.

[2] though in spirit, i feel like a student too.

another place, another talk.

there's something soothing about traveling for a conference. i was just a "student" at the previous conference and didn't do any organizing ..

.. in fact, i was ineffective and shoo-ed away from what few duties were given to me ..

.. but there's some charm in flopping on a hotel room bed after a long day of talks, or trying out a new restaurant or how this university caters a reception.

---

i'm also looking forward to giving this talk. the material is more standard to the audience. it's not like my thesis, where i have to explain everything, where what is standard for me is new for everyone else, and where i never really tell all my theorems.

ah well. it doesn't matter anyway, and it's not good to boast.
then again, it's not good to complain excessively, either,

so i'll shut up now, about that.

---

i like the math in this next talk. it's a good story.
then again, that's all it will be: a story.

i'll state one theorem i once proved ..more like a computation, really.. but will mostly draw connections from a few different parts of mathematics. there won't be many gory details. that makes for a good talk, of course ..

.. but not for a paper.

i still worry about writing it -- that i haven't proven enough new theorems, and that it's a story that everyone already knows.

even if i'm wrong about that, i still think i'm the wrong person to write it. i won't ever know the full story and how everything fits together. i can name a half-dozen senior profs, some emeriti, that could tell the whole story and tell it properly. my computation is obvious; ask any of them the problem, and they could have proven it years ago ..

.. even before i was born. the tools were all there then, and my part is far from sophisticated. i can't shake the feeling that i'm a young upstart who steals the stories of others and presents it as his own.

---

i'll write something about it: a paper, i mean. it was one of the promises i made to the advisor. otherwise i might have set it in a drawer on a shelf, left it in the back of a closet for a while.

it was something we disagreed about. i wouldn't have abandoned it, but perhaps entrusted it back to the advisor. he would have written it reluctantly but wonderfully, saw new connections, and made a great work out of it.

it's a good story. someone should tell it.
i guess it has to be me, then.

last week's conference; a retrospective.

some outcomes are inevitable. the conference is over, and subsequently,

1. my coffee intake has doubled (or so),
   
2. i've ceased exercising altogether,
   
3. i'm used to waking up early, having had done so willingly and over the course of one week.

then again, this was no ordinary conference. it was in memory of the advisor -- my late advisor -- so i suppose i should say anything that could possibly trivialise it.

---

it was well-attended;
i met new people and saw old friends and colleagues.

it was announced very early by the conference organizers who are the advisor's students, past and present. all of us were in attendance.

whether i would have or not, this made it very difficult for me to disappear into the shadows of east hall. admittedly, i tried. i only succeeded -- albeit partially -- during one afternoon, when there were no talks and the conference participants made their own way into ann arbor.

as a result, there was very little time (or rather, space in my preoccupied mind) to sort out thesis corrections and edits.

---

there were many occasions where people greeted me by name, and i had never met them. admittedly again, this really unnerved me.

i suppose that it taught me character and good graces. everyone asked me my status as a student and subsequently if i had a job in the fall. though i remain excited about that future, saying so -- repeatedly -- is less exciting.

i imagined making a t-shirt, where the front would read "yes, i defended 2 weeks ago" and where the back would read "i will be a postdoc at ______."

i know thatit's not fair to mistreat people if they simply don't know what i know. i guess i just bore easily.

---

i abandoned all intentions of discussing mathematics with anyone except

• those whom i promised, months ago, a few mathematical conversations;
  
• friends who were inconvenienced by my wrongful decisions;
  
• mathematicians whose work i've cited in my thesis.

it's unwise to be snobbish at my age, i know;
then again, if you had the thesis corrections i did,
the lack of time that i have,
trust me: you would do the same.

something's wrong with my invisibility cloak.

i've concluded something.

of all the times to attend a conference, this month and year ranks as the most inopportune. it feels petulant to give this as a reason, but i have thesis corrections to do and no time to do them [1]. next week is another conference and a similar lack of time.

it's not just the corrections. there are indirect consequences.

i had hoped that the next time i attend a conference, i'd have more questions in mind and more inclination to talk to people, possibly foster collaborations .. in general, be more interested and involved.

instead, my thesis consumes my thoughts, and i have to remind myself to be hospitable. i should remember that my friends and colleagues are here, that they're here when i am here, and after this year this will become a very rare thing.

---

it could be the size of the conference,
but something about it makes me inclined to edge away.

i felt the same way last august in helsinki. i felt like saying nothing and being ignored. this time around, it seems much more difficult.

---

so i think i greatly misplanned things, this may. despite my best efforts to assure people that it was all right to attend the other parallel section and to miss my talk --

as i've said before, in all honesty, and will say again, "if i wasn't giving my own talk, i'd attend that one!"

-- friends and acquaintances have apologized and promised to hear it next week. that's quite flattering and more than considerate, but there's a problem.

i'm not giving the same talk:
it will be about analysis, but not in the same subfield.

it's about something completely different: some work i did with the advisor about a thesis problem which never became a thesis.

a friend of mine even went to my talk on monday because next week, he and i will have the same time slot and give talks in parallel sessions. he made all that effort and he'll still not hear all that i have to say for these two weeks.

argh......

there seems a protocol for back-to-back conferences of which i was ignorant -- that it's okay to give roughly the same talk. somehow i thought the opposite principle was true -- that one should not bore the audience with much of the same.

it just goes to show you: my talks never go right at conferences.


[1] that's not quite true.
tomorrow (wednesday) afternoon is free of talks;

i might agree to meet people in the evening -- there's a party planned -- and disappear for a few hours to LaTeX and be frustrated.

before the math, drinks.

day 1 of the conference starts tomorrow, but in a way it's already begun. visitors have arrived today and tonight and i met them at the bar, just earlier. three things come to mind:

1. it's good to see friends again. i haven't traveled much since last summer, and the last well-attended event that i attended was inherently a tragic one. come to think of it, so is this one.
   
   it is a memorial conference, after all.
   
   on the other hand, there are explicit mathematics involved, this time. that has a way of smoothening things over .. at least for mathematicians.
   
   at any rate, i don't often see familiar mathematical faces to which i can start talking my sort of maths. it's been five long years in ann arbor, amongst algebraic geometers. it's nice to be able to have a conversation about analysis again.
   
   
   
2. when someone hears that you've just defended a thesis, it's very similar to someone hearing that it's your birthday or that you've had a birthday recently.
   
   there are cheers and "how does it feel" sort of questions.
   i've thought about it, and i'll say this:
   
   in this crowd, there are more ph.d's than not;
   you have all gone through the same ordeal and success.
   
   let's not make much of this; i now happen to be one of you,
   and i just happened to have joined you recently.
   
   on the other hand, thanks!
   you know how to make someone feel welcome. (:
   
   
   
3. i really have to get better at answering the question, "so what is your thesis about?"
   
   tonight someone asked me, and it took a minute to think of an answer. fortunately, the mathematician who asked the question had heard of my area, and i didn't have to start from scratch.
   
   i might not be as fortunate next time:
   something to work on, then!
   

also, evidently there are now some "tall tales" circulating about how my defense went. so for you readers: if you hear something interesting about it, it's probably not true.

yes, many people attended,
yes, i went overtime,
yes, there were many questions,

but that's mostly it.

preparations and priorities.

today hasn't been very productive;
i can't afford many of these types of days, for a while.

then again, i'd probably be much more productive if i'd stop worrying and just keep working. fear and worry can cripple the mind, as follows:

when you have so many things to do,
when you have so little time left,
well .. what do you do first?
are you sure that you wouldn't be more efficient if you do <this> instead?


in such cases, it's good to have deadlines, because they force your hand towards priorities. for example, on monday i'm slated to talk.

this means that i should write the talk today -- which i am doing now -- then sleep on it, and revise it tomorrow. maybe ..just maybe.. it will be ready by monday.


ah, well. i should be fine, either way.

• if the talk goes well, then great;
  
  
• if the talk goes badly, then at least my friends' talks will look even better by comparison. nobody will laud over me after my talk, which means that i can disappear more easily and get more work done.

people have told me to be more optimistic, after all. q:

we, the mathematical diaspora.

just now there is a fire alarm in east hall, where resides the mathematics department and in particular, my office.

sighing, i look at my desk. it's probably not a real fire, i think to myself, but just in case .. so this is what i bring with me, in this order:

1. my laptop, fully charged,
   
2. thesis corrections from my committee chair,
   
3. my copy of federer's geometric measure theory,
   
4. my pens,
   
5. my cell phone,
   
6. my watch,
   

and putting all of these things in my bookbag. walking over to the coffee pot, there remains some of that pleasant brew.

i pour myself a cup of coffee, take a sip, and then saunter out the nearest exit.

---

there's no space at espresso royale, inside or outside. all the mathematicians and psychologists have taken refuge there [1]. thinking to work outside, i realize that this cursèd sun makes it impossible to view my laptop screen.

so for a while, i chat amicably with other math grads that i don't often see.

then one prof sees me and asks me how i'm doing, what pittsburgh is like. then he tells me that he will attend my talk on monday. cr@p. now i have to give a good talk.

it's not just him, of course, but still .. \:



so now i risk the UGLi [2]. yes, i'm blogging, but now i'm getting back to work ..

.. because if i don't get enough thesis corrections done now, then i'll lose time preparing a talk and attending other talks at the conference and then nothing will be done.

[1] on one side of east hall, there is the mathematics department. the other side is the psychology department. we don't mix much.

[2] i.e. the shapiro undergraduate library.





addendum (@ 3:56pm): back in east hall; the alarms are quiet. it's strangelyy comforting. i suppose that birds are allowed to prefer certain bars over others, for their cages. q:

as for what i left behind:

linear operators, volume 1 by dunford & schwarz,
functional analysis by rudin,
lipschitz algebras by weaver,
my bicycle helmet,

"don't pay attention to the man behind the curtain (read: office door)"

at this point it is a race against time. unlike most races of sportsmanlike conduct, however, i don't think i will be very scrupulous anymore.

---

i have a deadline for my graduation requirements: may 27th.

i don't expect that the very last day will be available; if other matriculating grad students are anything like me, they will be in similar, dire straits!

i've received comments and corrections from 60 pages of my thesis. while working on those, i am waiting on similar feedback for 62 more pages.

i never thought i could write that much;
now i wish i didn't.

i also have two conferences between now and then. for one of them, i have "home court" advantage; it will be the late advisor's memorial conference.

in other words: if i must, then i can disappear for a while and work, return to the conference for official duties ..

(like other michigan grad students, i am helping out with some errands for the conference)

.. and then vanish again.

so, caveat emptor: if you are attending next week's conference in ann arbor, then apart from monday, thursday afternoon, and friday, i might not be there.

if i promised that i'd see you here and chat, next week ..
.. well, i never thought i'd say this, but i do take appointments.

seriously.

in fact, i think i'm having lunch and talking p-harmonic mappings with one of you readers, next thursday. for some reason, i knew in advance that my life would not be my own, even after my defense \:

dumb day.

today has been a "feeling stupid" sort of day.

1. this morning i spent more time (than i'd like to admit) computing a few basic derivatives that you might see in Calculus I.
   
   at the time i couldn't see why a particular function was 1-Lipschitz and i didn't like the reason that a book told me. i still don't like the reason, but i see why it's true.
   
   it took a few times to get that computation right, though. i suppose that say something about how long it's been, since last i taught calculus.
   
   
2. i asked the supervisor a dumb question today. it was dumb because i couldn't remember a line of argument he told me yesterday, and i couldn't figure it out for myself.
   
   it was one of those "once you write it down" sort of arguments. i might often underplay my skills at maths, but trust me on this one: i was being dense.
   

oh well.

i now see how to fix things, and i see them well enough that i can LaTeX. that's the important thing, anyway.

there was calm. now: the storm.

time is always against us.
the defense is done: so what?

      here there be thesis corrections to make,
      and conferences talks to write

there is already a lot of red-inked comments that i have to reconcile.

may 27th is not the deadline, not three weeks really:
it's more like one week's time.

..
well,
this should be interesting.


EDIT - 06 may 08, 12:50am: earlier today i felt like the white rabbit from "alice in wonderland" -- running around, running out of time.

life after a defense.

i had promised myself that i wouldn't do any work yesterday and today, but i ended up breaking that promise ..

.. on both days.

oh well. at least i didn't do any LaTeX until today. besides, there's not much time before the rackham graduate school deadlines, anyway.

---

earlier today i was walking past the first-year grad student offices. the doors were closed and the interiors looked dark.

for some reason, that sight relieved me. there might be qualifying exams soon, but at least the younger kids know enough not to lurk in their offices, all the time.

endgame: stand and deliver.

so yesterday was the defense. all of the committee arrived on time, including the cognate member [1].

there was a large audience, too. the 20 seats in the room were taken, and 5-7 more stood or sat on the wide window ledge (in the back of the room).

admittedly, i hadn't expected this. many people had told me that they would attend, but i thought they were saying that for support. they all came, after all!

there were a lot of questions, so it actually felt like a defense.

i suppose it is a good thing. it was pointed out to me that questions indicate that some people are indeed listening and that they understand you well enough to ask their questions.

on the other hand, some of these were questions like:

"does the module have torsion?"
whereas i couldn't remember what torsion was; it was mildly embarrassing.

also, apparently i was working with a different notion of rank than what most people do. so i was asked, "wait. so you mean that the module has rank at most N?"

"er: it's not a free module," i replied.

they added, "you can define rank just with linear independence."

"oh," i noted.

anyway, i was nervous and i went over my allotted time, and barely gave any intuition why my main result makes sense.

then there were even more questions.

when it was over, we left the room so that the committee could make a decision.

.. a few,
LONG
minutes
later ..

the committee members walked out of the room,
each shook my hand,
and i became a doctor.


there are thesis corrections still to make, but it's done. the forms are now at rackham and it's a matter of paperwork.

[1] according to rackham graduate school rules & regulations at the U of M, a dissertation committee must include one faculty member outside of your home department. interestingly enough, the rules allow for one committee member not to attend your defense as long as it is not the cognate member.

t-minus 18.5 hours.

everyone's been asking, so ..

yes, tomorrow's the day;
i defend my thesis tomorrow.

no: i am panicking.
the committee is composed of very nice men, but i'm still panicking.