preparing for class, part 3: lecture notes.

that monograph thing that i mentioned earlier is just an idea, really;
i don't know if i should be the one who would write such a thing.

to clarify, it's not that i don't think a monograph should exist on the subject [2]. it's just that someone more senior and established in the field should do it [1] .. or rather, someone more trustworthy and with a better view of the Big Picture, both in regards to the field as to how it started and how it is now.

anyway, i don't trust myself to do it .. that is, to do a good job with it.

the last time i tried to write an exposition, it was about the p-Laplace equation and the first draft was such a mess that i despaired of it ever seeing print.

most of it is a re-telling of DιBenedetto's story, of course, but with an emphasis on techniques that can easily be extended to both non-smooth spaces and functions on them. for those of you who know the field, you probably know there are enough of these kinds of expositions so that a better one than mine exists and is accessible.
..
..

.. maybe i'm being too rigid in my outlook, though.

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thinking about it, the world's gone sufficiently digital as to allow a continuum of document types. on one end, we have well-polished textbooks and peer-reviewed research articles .. but there are less formal ways, too.

• take, for example, this prιmer on differentιable structures on metrιc spaces. maybe it will see print in a journal, maybe not (though i hope it will), but as it exists now, i think it's a great resource. it serves the very useful purpose of a clear, concise exposition without suffering the troubles of formal publication.
• a similar resource is a technical report that the advisor wrote, years ago: i still favor it over the standard GMT references, when thinking about fΙat currents. the topics are based on .. come to think of it, a series of lectures he gave one august.

a final decision can wait, i guess. the publication of monographs seems such a formal affair to consider. i think i'll start small. i've already developed the practice of sharing my handwrit talk notes with audience participants, and occasionally posting scans of them on my homepage.

being that the contents of these lectures will be a little substantial, maybe it will be good to have them in a digital, searchable format and easily accessible on the web ..

.. so it sounds like a wiki is in order!





[1] then again, colleagues of mine have co-written a book about some topics on metric space geometry. one of them defended his ph.d. the same year as i did .. so if he can do it, then maybe i can too?

[2] to be honest, i think there are too many books and papers out there. this is related to job candidates essentially being required to publish a lot of papers .. and with teaching loads as they are, these days, odds are that not every paper will be a strong one. maybe it's not a bad idea to show restraint and buck the culture .. because if we don't, then this is only going to get worse!