Question: I wish to use one of your course notes as the text for my course. Is it OK for each of my students to download it and print it out?
Answer: Yes, that's OK.
Question: I wish to hand out copies of the chapter on free groups from your Group Theory notes to my topology class. Is this OK?
Answer: Yes, provided you don't charge for them.
Question: Can you reformat your notes so that I can read them on my six-inch Kindle?
Answer: I did this with the three most popular sets of notes. It's easy to reformat them --- all you need to do is remove the margins and change the print area and fonts to roughly double the number of pages. However, then many tables and math displays don't fit, and it takes to time to fix them. Sometime, I'll produce versions for ten-inch readers. This shouldn't cause so many problems.
Question: Can you produce an epub or azw version of the notes?
Answer: No. There are programs that translate TeX into epub, but they don't work very well, and the result requires a lot of manual editing. There are many complaints about the mathematics in the books Amazon sells.
Question: Do you plan to publish the notes as books.
Answer: Perhaps some. My intention for each set of notes is to either publish it as book or make the TeX-code available under a licence which allows people to do more-or-less what they wish with it so long as they make their TeX-code available under the same terms.
Also, I plan to put some of the notes on Deep Blue where they will remain permanently available, with a permanent URL.
Question: What if you get run over by a big Mack truck?
Answer: I won't care. That's the only good thing about getting run over by a big Mack truck --- you no longer care.
Question: Does the Hodge conjecture have any applications? (Majid Hadian, November 4, 2013).
Answer: Most Shimura varieties (those of abelian type
with rational weight) are known to be moduli varieties for
abelian motives with Hodge cycle structure. Thanks to
Deligne's theorem on Hodge cycles on abelian varieties, this
makes sense over any field of characteristic zero, and can
be used to realize the canonical models as moduli varieties.
If one knew the Hodge conjecture, this description would
persist into characteristic p and would be very helpful in
proving the Langlands-Rapoport conjecture (L&R arrived at
the statement of their conjecture by assuming that the
Shimura variety mod p is a moduli variety for motives). This
is all discussed in my second article at the Seattle motives
More specifically, L&R prove their conjecture in their paper for Shimura varieties of PEL type assuming (a) the Hodge conjecture for CM-varieties; (b) the Tate conjecture for abelian varieties over finite fields; (c) the Hodge standard conjecture for abelian varieties over finite fields. I proved that (a) implies (b) and (c), so all one needs is (a) to make their proof work word for word. (This is where I'm permanently stuck, but the conjectural theory of rational Tate classes is designed to get around (a).)
Once one has the L-R conjecture, the main obstruction to proving Langlands's conjecture that the zeta function of the Shimura variety is automorphic was always the fundamental lemma, but this has now vanished.