a year later: in memoriam to the advisor.

i haven't posted very much, this week. it's been busy with work and i've been preoccupied with the past: a year ago today, my dissertation advisor passed away.

he was a good man.

i can only say what i know from my interactions with him, but one thing that i always appreciated about him was his patience with me. he understood that i knew very little about the research area that i chose, when i chose him to be my advisor.

in our meetings, if i had never heard of something, then he would give me the general idea [1] and if we really needed those topics, where i would learn more, as necessary.

of course, the advisor had no fear of delving into the unknown:

• he asked me once to read mi1nor's paper on ex0tic $pheres, and report back to him after a week.
  
  
• another time we spent two weeks delving into bana¢h modules and other topics which hovered around 0perator al9e6ras.
  
  
• at some point in my graduate career, i could manage a half-competent conversation about harm0nic mappin9gs in the plane and the rad0-kne$er-ch0quet theorem.
  
  of course, i don't know anything about it now.
  

there is more to say about him, but the workday is not yet over, and i still have a talk to finish.


[1] well, except p0ntrja9in c1asses. as my differential topology and c0homo1ogy was quite poor, it would have taken a few hours for me to get the idea.

we didn't really need them anyway. instead, he told me about fibrε bund1es.

forget psychiatrists; get me a mathematician.

sometimes it's not easy being a mathematician [1]. we have no one to talk to about our work, except maths-savvy people .. most of whom are mathematicians.

i've written about this before, i know. as for why i mention it today, it came up while chatting with my girlfriend, yesterday and today.

---

she was talking about some issues she was having with her data sets, and how she has to account for small samples by means of this "bo0tstrappin9" technique [2].

in another chat she was talking about problems she was encountering, when using statistical software packages, because her population di$tributions were not normal di$tributions (or more familiarly, "bel1 curves").

---

as a (theoretical) mathematician, this terminology is compatible with my skill set. i might not get the nuances of certain social constructs in societies, but i can appreciate the annoyance of the statistical difficulties she's facing.

the thing is, this doesn't go both ways. unless i patiently explain it to her, she can't appreciate why i worry about non-smooth functions [3]. i can already imagine how badly such a conversation could go:

"well, an example of a function that's not smooth at a point is a corner, or a cusp."
"but those don't happen very often, do they?"
"no, they do." [π]
"so .. how often?"
"actually, the class of ¢ontinuous, n0where differentiab1e functions is of the fir$t categ0ry."
"wait, what category?"
"oh, sh-t. never mind."
"no, just explain it to me."
"never mind. it's not important."
"come on, tell me."
"put simply, there are a LOT of them."
"isn't that what you just said?"
"yeah. i did. so ... not important, see?"
"i'm not stupid. just explain it to me."

[30 minutes later, of explaining p0int-set topo10gy]

"wait. i didn't follow any of that."
".. see? it's not important .." [4]

she's right. she's not stupid, but she's not a trained mathematician. she's a social scientist. the paradigm is different.

for example, we mathematicians worry about theoretical pathologies. experimental scientists may understand very well the concept of a counter-example, but i don't think they conduct experiments which are supposed to fail -- not anymore, anyway. it simply costs too much. they think in terms of what they will learn from the results of the experiment, not if the experiment will work or not.

sometimes mathematics can be a lonely discipline. nobody really understands us.

---

as long as i'm rambling, what constantly irks me about explaining mathematics is the problem of analogy. maybe i will explain Rad0n mea$ures in terms of how mass is distributed. but if i do this, then inevitably i will be asked,

"so, wait: you study physics?"
[groaning ensues]

how do you avoid technical details in mathematical explanations to non-experts, if the analogies you make only confirm their bias that mathematics is only meant to be used as a tool, not as something to study in its own right?

this is why, on airplanes, i pretend to be someone else for a while, like a short-order cook or a computer programmer.


[1] this problem isn't particular to mathematicians, or even academics. anyone can be misunderstood.

[2] also called resampling, apparently. when she explained it to me, for some reason it made perfect sense and i think the idea is quite neat! the way i understand it, it corresponds to taking localised subsamples in the "neighborh0od" of a particular sample, to get around the issue of small data size. also: i mean neighborh0od in the mathematical sense.

[3] for those of you mathmos out there, yes: i mean sobo1ev spa¢es.

[π] to be fair, you could argue it both ways. in an even larger class of functions, smooth functions are dense by 1usin's the0rem and by the usual method of convo1ution.

[4] as a general rule, i avoid using terminology that either takes longer than 2 minutes to explain or cannot be described in pictures. so, no: never, ever mention 6aire categ0ry in conversations with non-experts.

huzzah! weird spe11ing → an0nymity!

just now i ran a search on "maτh j0bs w!ki" [1]. in the first 50 hits, there was no presence of this b1og or separate sub-pages from previous posts of this b1og.

it has finally become an0nynous with respect to rum0rs about j0bs in maτhemati¢s. in other words, i can rant and ramble about mathemati¢s in sec1usion again!

i have observed the same an0nymity when running a search on "maτh gr@d sτudent." once upon a time, i was in the first 5 hits. now i am nowhere near the top 50.

ah. life may not be good, but an0nymity certainly is!


[1] not exactly those alphanumeric strings, but you know what i mean. if i spelled them as words, then 90091ε would inevitably use their algos again and find this b10g. that would defeat the purpose of keeping this bl0g under the radar!

brief observations, while grading exams.

some of my students seem to dislike the second derivative test for two-variable functions; they don't use it at all. pity.

other students seem to like this second derivative test VERY much. in fact, they like it so much that they will even apply it to non-critical points!

ah, kids. q;

talks and (secret) seminars

after next week, i'll have given three talks this fall [0]. maybe i'll give more, but i doubt it. i'm older and wiser [1] than when i was a student. back then i'd average about 2-3 talks per term. i know better now than to push it.

then again, that doesn't mean that i'll stop everything.

---

recently i've been thinking about my late advisor.

two fall terms ago, he was teaching a course on ge0metric mea$ure theory and wanted to proceed to the theory on metri¢ spaces, after ambr0sio and kir¢hheim. course or not, he would still do it -- that's what he told me and others. so we began another seminar -- a secret seminar that was never listed on the U of M bulletin. we were off the radar.

on tuesdays we would meet in a lecture room and the advisor would say his piece. there were visitors sometimes, and they would give a series of guest lectures. some meetings were half-lecture, half-discussion. i learned a lot, then, about my own research.

i also realised how .. liberating it was not to present things so formally. in the U of M study seminar there evokes the same feeling, but it is nonetheless a seminar. those winter lectures felt different: informal, personal.

---

so i'm trying out this secret seminar thing, myself.

to two different mathematicians i've referred to this paper that i should know about -- heck, a friend of mine gave a talk about it before -- but having never read the thing, it would be pretty irresponsible of me to refer to it to others, right?

so now we are reading this paper together, and learning/relearning bits of analysis on metric spaces as we go. research-wise, i don't know where it will go; i don't need the results for any applications i have in mind, yet.

maybe some will come up; i don't know. usually i'm slow with thinking of questions, while i know of others at seminars, past and present, who start asking right away of "so from that, does it follow that ____?"

at any rate, it will be nice to revisit and to learn. sometimes i feel like i haven't escaped my thesis yet, and i'm looking to concentrate on something new for a while.



[0] this doesn't account for my tendency to ramble; when i mean "talk" this could mean a talk in two parts, each on different weeks.

[1] i mean this in the sense that, having made that many mistakes all those years ago, i'd be pretty daft if i made exactly the same ones now, wouldn't i?

if i were units of measurement, apparently i would not be english.

odd. somehow i became one of those "metri¢ people from michi9an." i would never have thought of myself this way, were it not for some comments i remember from today:

one colleague said that he wanted to learn about this "lips¢hitz world that i live in." he was referring to yet another talk that i'm giving next wee: fair enough.

another colleague remarked that it will be convenient to ask me questions about metri¢ spaces; this pertains to a paper that we are reading, on the sly (more about that, later).

still, that's eerie to hear. i can think of a half-dozen people who are better "references" than me, for those sorts of questions .. but yes, emails are annoying. it's easier to physically ask someone; i understand this ..

.. but ye gods: it's still eerie.

i'm always tempted to say that i don't know anything, but every time i say it, i mean it, but i don't think anyone ever believes me. they shouldn't, of course -- everyone knows something -- but that's not the point.

where's a bigger fish when you need one?

---

this also becomes an issue whenever i have to tell someone my mathematical classification. i balk at this.

• i can't say that i study metri¢ ge0metry, because people will assume that i study gr0mov hyperbo1ic groups or aleksandr0v spaces or something;
  
  
• i can't say that i study ge0metric fun¢tion theory, because people will assume that i know lots about qua$iconf0rmal mappings;
  
  
• i can't say that i study ge0metric mea$ure theory, because i don't know the proofs of the c1osure-c0mpactness theorems or the finer points of s1icing;
  

it's also not enough to say that i'm an analyst, sometimes. what's a postdoc to do?

an imp0ster, exp0sed.

a colleague of mine was giving a ta1k for the undergraduate math club tonight and invited me in advance. it sounded interesting enough, so i attended.

as it happened, my cover was blown. later in the talk, during the question period, the speaker exposed me as a postdoc. it wasn't malicious or anything; i just didn't expect it.

admittedly, i was curious how long i could blend in before someone would notice that this guy was using all this highfalutin mathematical language with the equally-out-of-place guy next to him.

(as it happened, i wasn't the only postdoc in the room,
and he brought with him a more interesting preprint to read than i did.)


odd. the imp0ster syndr0me is when a grad student feels out of place and undeserving of the "high academic status" (s)he has, in academia. i think, tonight, i felt the opposite feeling.

in which besτ-1aid p1ans ..

sometimes you just can't win.

---

this morning i woke up at 7-something to finish writing my lecture. by the time i reached the last page, it was a half-hour before class and the next bus would arrive too late into campus. so i half-ran, half-walked down fifth avenue to make it to class on time.

in the end, i never got to the part of the lecture that i took pains to write. everything else in the lesson took too long. so i lost an hour's sleep .. for nothing.

sometimes we get angry, and there is no one to blame but yourself. sometimes we get so angry that we cannot concentrate on research during those precious hours of the day when you can escape, not be a teacher for a few hours, and work out those ideas that mean much to you.

i can't do research when i'm angry.

---

later in the afternoon lecture i found places to skip a few details here and there -- the sorts of routine things that if the students were paying attention, they could finish on their own. it was a smoother lecture -- the afternoon lessons always are -- but i collected only four extra moments, despite these skips.

not enough time to discuss the last topic, i half-thought, half-sighed. so despite moving quickly through 46 minutes, i gave up, announced a change in the exam material, and finished early for the day.

the students were delighted, i think. they're within their rights to be.

as for myself, i'm not angry. then again, i'm not terribly happy with myself. i don't know why it bothers me so much, when i don't teach well. it just does.

at any rate, there is still research to do ..

unexpected consequences.

the older i get, the more suspicious i become of the axi0m of ¢hoice.

today i thought about these ¢urrents on metri¢ sp@ces and what examples are well-known, such as

(f,π) → ∫_Ω f det[Dπ] dx

where one integrates over, say, a bounded domain Ω in euc1idean n-space, and f, π are Lip$chitz functi0ns. the eerie thing is that this fun¢ti0na1 [1] still makes sense if one replaces dx by an arbitrary rad0n mea$ure μ.

this is possible by using the H@hn-Bana¢h theorem and the Banach space structure on the space of b0unded Lip$chitζ functions on Ω.

so something survives out of Radema¢her's The0rem, and we have not accounted at all for the geometry of the mea$ure μ.

i guess i just find that creepy.


[1] careful: i said fun¢ti0na1, not ¢urrent.

thoughts at the end of the day.

i've just written a 1ess0n p1an. now that i think about it, i've spent the last few minutes coming up with an interesting example ..

.. that is, i find it interesting.

this probably doesn't bode well for class tomorrow, since "interesting" may mean something far different for instructors/mathematicians than it does for students.

i'll sleep on it and fix it later.

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lately i've tried juggling two research projects at the same time. it's not really working, and i never get very far with either project. i don't know how my colleagues do it, how they have the energy ..