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Below are the 25 most recent journal entries.

	2009.07.06  17.29 A Chess Game I played in a tournament in Sacramento this weekend. Here is my best game from the event. Aditya Kumar (1800) vs. Simon Rubinstein-Salzedo (1905), Sacramento Chess Club, Round 5, July 5, 2009. 1. d4 f5 2. c4 Nf6 3. Nc3 g6 4. e3 4. g3 is more common, but this line is fine as well. 4... Bg7 5. Bd3 0-0 6. Nf3 d6 7. 0-0 Nc6 8. a3? I am playing for the move ...e5, so my opponent should prevent me from making this move, or at least extract concessions if I do make it. Better is 8. d5 Ne5 9. Nxe5 dxe5, when I have a pawn on e5, but at the cost of a compromised pawn structure. Still, I'd be happy to play that position with black. 8... e5 9. d5 Ne7 10. e4 f4 11. h3 One advantage of playing this system with white rather than the more standard system with g3 and Bg2 is that h3 is not quite as weakening here. My plan is to get my pawns to h5 and g4 eventually and break through against my opponent's king. This move may slow me down a bit, and it allows him to set up a big of a fortress, which I will find difficult to break through. White's main idea here is to expand on the queenside with moves like b4, Rb1, Bb2, and c5, and try to make my queenside collapse. This is an especially appealing option for him, since my pieces will be heading over the queenside to attack the white king. Therefore, if he can avoid disaster on the kingside, I may find my pieces too far away to fight off an invasion on the queenside. So, let's see what happened. 11...h6 12. b4 g5 13. c5 a6 The point of this move is to slow down his queenside invasion a bit. A move I'd like to play is Qe8, but after Nb5, it's tough to fend off a quick invasion on the queenside. So, a6 prevents Nb5 and unties my queen from defense of c7. 14. Bb2 Qe8 15. cxd6 cxd6 16. Nh2 h5 17. Be2 Qg6 18. f3 So, he seems to be defending g4 adequately. I thought I needed to bring in one extra piece in order for the ...g4 break to work. However, 18...g4 is already possible, since the pawn on e4 is not defended too well. One sensible line is 18...g4 19. fxg4 hxg4 20. Nxg4 Nxe4 21. Nxe4 Qxe4 22. Bf3 Qg6 23. Rc1 Nf5 (not 23...Bf5? 24. Rc7 e4 25. Bxg7 Qxg7 26. Bxe4! Bxe4 27. Re1, and white is winning), which is roughly equal. 18... Kh7 19. Re1 Neg8 20. Kf2 Nh6 Finally, I have enough pieces gathered to play g4. 21. Rh1 Kg8 22. Na4 g4 23. hxg4 hxg4 24. Nf1 b5?! I looked at 24...Nxe4+ 25. fxe4 f3 26. gxf3 gxf3 27. Bxf3 for a long time but convinced myself that it wouldn't work. But it does. After 27...Bg4 28. Nd2 Bxf3 29. Nxf3 Ng4+ 30. Ke1 Qxe4+ 31. Qe2 Qxf3 32. Qxf3 Rxf3, black is up a pawn and should win without too much difficulty. But my computer finds the response 26. Ng3 fxe2+ 27. Qxe2, which it claims is roughly equal. Still, as we shall see soon, there are problems with this move I played. 25. Nb6 Rb8 26. Nxc8 Rbxc8 27. a4 This move wins a pawn, at least, sort of. But now 27...Nxe4+ really works. After 28. fxe4 f3 29. gxf3 (or 29. Ng3 fxe2+ 30. Kxe2 Rc4! is great for black; this is the difference!) gxf3 30. Bxf3 Qxe4 31. Ne3 Rxf3+ 32. Qxf3 Rf8, black is easily winning. I missed this line, but I thought that if I could convince his bishop to leave e2, then everything would work perfectly. So, 27...Rf7 Now I can think about playing Rb7 to defend the pawn, followed by Rcb8 if necessary. 28. axb5 axb5 29. Bxb5 Nxe4+ Finally. 30. fxe4 Qxe4 31. Bd3 Probably the best defense. 31...g3+ 32. Kg1 Qxb4 33. Rxh6! I overlooked this move when playing 29...Nxe4+, so I was panicked. The first point is that 33...Bxh6? loses to 34. Qg4+, forking the king and rook. The second point is that 33...Qc5+ (defending the rook) 34. Kh1 Bxh6 is met by 35. Rc1, again winning for white. The best moves seem to be 33...Qxb2, and the move I played, namely 33... f3! Cutting off the queen from g4 while retaining my threats of Qxb2, Bh6, and 34...Qc5+ 35. Kh1 Qf2 with the idea of taking on g2 with checkmate. 34. Bc1?? 34. Bg6 seems to save white. A possible line is 34...Rf4 35. Bh7+ Kf8 36. Rh3 (forced, to prevent 36...f2+ 37. Kh1 Rh4+, when 38. Rxf4 fails to 38...Qxh4+ 39. Nh2 Qxh2#) Qxb2 37. Rxg3 e4, after which a draw is the most likely result, at least, if played by much stronger players. Now I finish him off quickly. 34...Bxh6 35. gxf3 Qd4+ 36. Kh1 Qxa1 37. Bh7+ Rxh7 38. f4 Bxf4 39. Kg2 Rh2+ I played this to trade off a bunch of pieces. If 40. Nxh2, then 40...Qa2+ 41. Bd2 Qxd2+ 42. Qxd2 Bxd2, and white needs to resign as soon as possible, if not sooner. 40. Kg1 Qa7+ 41. Ne3 Bxe3+ White resigns. I missed a few strong moves for both sides when I was sitting at the board, but they were in very complex positions with lots of possibilities. I'm still very happy with my play in this game. But not in the rest of the tournament.

	2009.06.13  17.23 Comfort I think I'm too comfortable at the moment. I need some new interesting contrary ideas to think about. Can anyone give me some suggestions? Preferably not politics. There must be far more ways in which society is wrong than just the ones I've already figured out. Music: Haydn ``London'' Symphony #104

	2009.03.26  16.05 Laptopless I'm leaving tomorrow to go to a conference in Israel, without a computer. How wonderful it must be not to be reachable for an extended period of time, and to have no (or fewer, anyway) distractions.

	2009.02.04  19.31 What I learned today The étale fundamental group of the projective line over Q with three points deleted may be the most interesting object in mathematics.

	2009.01.27  18.47 Being right Maybe one of these days, I will finally figure out that it's okay to choose not to be right. Occasionally.

	2008.12.24  16.20 Encoding Information I finished reading Katherine Neville's new novel The Fire yesterday. It's good and worth a read, but its prequel, The Eight, is a masterpiece. Anyway, I spent most of the time thinking about encoding information. (I've thought about this a lot before reading this book too.) In particular, it is interesting to think about how much information can be encoded into some (different) string of characters. When I was at Santa Barbara, Rabbi Mendel told me a story. The entire story is not terribly relevant, but the crux was that two people had a falling-out over whether one Torah portion could contain all the information about the universe. The skeptic asked his teacher to find him in the Torah portion, and the teacher said that his name was spelled out as the second letters of some set of consecutive words in the portion. I am unconvinced. Of course if you have enough letters, you can find various things spelled out, but presumably if someone is going to be decoding the message, that person will want some sort of criterion for determining whether any particular hidden message is intentional or not. In particular, one major criticism of Bible codes and other such nonsense codes is that they have no predictive power. I guess that's another way of saying that there's no way of telling whether something is intentionally encoded or not. Here is one example of a good code from The Eight: I have warned you but you will not listen. When you meet with danger, you should not hide your head in the sand -- there's a lot of sand in Algeria. The words are mostly meaningless; only of interest are the first words of each line. (The character figured this out accidentally.) Several codes in The Fire were notable, albeit much less convincingly executed. The first was a telephone number given as (615) 263-94. Decoding that is reasonable albeit maybe a bit of a stretch: two digits are missing, so one must figure out what they are. Well, rewriting the number as 61 52 63 94 and reversing each set gives 16 25 36 49, after which it's logical that the last set should be 64 (squares). I'll believe that someone who is good at dealing with encoded messages could have figured that out. The next was a message that read: WASHINGTON LUXURY CAR VIRGIN ISLES ELVIS LIVES AS ABOVE, SO BELOW The fourth line is easy to decode if you've been reading the book. (I didn't have any trouble with it.) The person who left the message is named Cat Velis. The first three are also pretty easy: Washington is DC, luxury car is LX, and Virgin Isles is VI (I'm not sure what that's supposed to mean exactly.) Well, those are all Roman numerals which come out to 666. That number keeps coming up in the book, although it isn't clear to me why. However, that's the wrong code, but I didn't really understand the logic behind the right one. And the last line I don't feel like trying to explain. There are a few more overly convoluted codes in the book, as well as people who know way too much. Go and read it; I won't tell you what happens, but read The Eight first. When he was teaching the algebraic number theory course I took a few years ago, Agboola said that the zeta function of a number field tells you everything you could want to know about the number field if only you can figure out how to ask. But in that case we like to know everything; nothing is encoded unintentionally. (And if you want to tell me happy things about zeta functions of number fields, I'd be glad to listen.)

	2008.10.28  07.44 Improvement Suddenly, and for reasons I don't understand very well, I'm a lot more satisfied with my life. I'm enjoying my classes (algebraic number theory, modular forms, and early recordings) and the Hartshorne group (we're supposed to solve all the problems in chapters 2--4, but it's turning into solving the problems we find interesting in chapters 2--4, which is probably still okay). I'm also starting to take on more projects. I'm co-organizing the Faculty Area of Research Seminar; yesterday we had our first talk. Even though it was about probability and applied math and PDEs, I found it really interesting and understandable. Next week we have a talk on low-dimensional topology. Last weekend I taught two classes at Stanford Splash, a program that allows Stanford students (or anyone, really) to teach classes on any subject to students in grades 7--12. I taught one on the Dutch defense in chess and one on combinatorial games. I'll be giving another talk on games to undergraduates next week, and I'd like to discuss lexicographic codes a bit in that one, if I have time. (Some of them might have seen the Sprague-Grundy theory before, but I highly doubt they will have seen this.) I'm also going to present something next week at the Putnam seminar that I went to when I was in high school (and once last year); I think I'll present a problem whose solution involves finite calculus. At some point I'll give a talk about Galois groups of extensions of local fields at the second-year seminar and a talk on either Tschirnhaus transformations or arithmetic dynamics (I'm not sure exactly what I'd say about it though) at the kiddie colloquium. So I'm glad to be interested in math again. I think the music class helps; it gives me something to do that isn't math. It's a lot of work though! Anyway, the weather looks perfect for a walk right now, so I'll head off to campus now.

	2008.08.17  15.52 Trust Now I know why they invented the written contract. Remind me never to trust anyone again. Music: Acis and Galatea

	2008.04.04  15.27 I passed quals. I may now return to my life and enjoyment of mathematics and everything else that I abandoned six months or so ago.

	2007.12.17  11.50 I have neglected this journal for over two months, so it's probably about time to post something. I have surprisingly little to say for myself; I managed to survive my first quarter of graduate school somehow. I wish I could say I did better than mere survival, but I feel that anything else would be a lie. I don't foresee next quarter as being much better. Spring quarter, however, could potentially be quite pleasant. Too bad I'll still be living in the same dreadful apartment then. At least I managed to do some actual mathematics yesterday, or at least start doing some. Ravi asked me if it is possible to generalize Conway's construction of nim fields (fields of order 2^2^n sitting inside \mathbb{N} with an unusual additive and multiplicative structure). I haven't checked that everything works properly, but I think I have a construction for fields of order p^q^n (p must be prime of course, and I think q probably needs to be prime as well, although I'm not certain about that). There is a game described in Winning Ways 3 with the right sort of additive structure. The multiplicative structure is harder to understand in terms of games (although it does show up occasionally). My general feeling is that this year is something of a setback in my mathematical career. As an undergraduate, I did what I wanted, took classes that I thought would be interesting and challenging, and got what I wanted out of them. This year, I take classes that someone else thinks I ought to take so that I end up knowing things that someone else thinks I should know. I understand that it's important for graduate students to know these things, but it would be nice if there were a bit more flexibility in it. Perhaps they could allow us to take one class of our own choosing and spread the required classes over two years. We might lose some of the community that we have (since most of us are in all the same classes), but at least it would be less painful that way. Fortunately, I'm taking a week off early next quarter to do arithmetic dynamics. I need to reread part of Silverman's book so that I don't demonstrate that I am a complete moron at the workshop. Mood: disappointed

	2007.10.05  19.53 Two weeks of classes So I've made it through the first two weeks of classes at Stanford. I find most them to be a lot less carefully worked out than the classes at Santa Barbara. In particular, we rarely bother to define terms or state the theorems we're going to need in the algebra class. That's fine for me since I already know this material, as do most (all?) of the other graduate students. But it's probably more difficult for undergraduates who haven't taken these courses before. Actually all the first-year courses are boring since I took all these classes already. It seems they might be less mandatory than I previously suspected, so I'm thinking about not taking algebraic topology next quarter since there is a really interesting class on class field theory and central simple algebras at the same time, which will surely be of more use to a number theorist than a bunch of topology I already mostly know. There is also a course on ergodic theory and combinatorics next quarter, and I don't think I can ignore it. Algebraic geometry is much more interesting, even though I have already seen the stuff we've done so far (categories and sheaves) before. It was really helpful to do a lot of problems about categories/diagram chasing, and I think it will be similarly helpful to solve problems about sheaves. I'm also going to be doing a reading class on arithmetic geometry (probably using either Lorenzini or Hindry and Silverman). Then there's the local Langlands seminar. Brian Conrad (who is coming to Stanford next year and will probably be my advisor) is running a seminar at Michigan, and he is having us run a parallel seminar here, presumably so that he can continue where he left off when he gets here. So far we've just talked about some background on local fields and Galois representations and stated the local Langlands correspondence for GL_2 in terms that we have yet to define. I'm also a course assistant for a basic calculus class. My first few office hours were very quiet, but today there was a veritable mob! I wonder if I can figure out a way not to have to repeat telling different people how to do the same problems. It seems like a difficult problem since some people come at the beginning of my office hours, and then others come at the end with the same questions. Anyway, I think they understand what I tell them. If not, they pretend they do. But maybe I said that about combinatorial game theory too (and indeed, some of them definitely did understand what I said; some didn't). Also, I was accepted to an AIM workshop on the uniform boundedness conjecture in arithmetic dynamics, so it would be helpful to review/learn some key results in arithmetic dynamics before January. I assume that this one will be more comprehensible than the one on the Tate conjecture (the statement of which I still do not understand), but I will still presumably be the least advanced participant in the workshop, so I should make an effort not to embarrass myself. Listening to operas in English is extremely fun, especially given these childish and silly translations. Stanford's Naxos subscription very kindly provides us with a good selection of operas in English translation. I must not let this prevent me from getting work done. Music: Rossini Barber of Seville (in English)

	2007.09.21  08.07 Stanford So I'm at Stanford now. The first few days here were very boring since I didn't know anyone, and I didn't have much to do except unpack and complain about how small the kitchen is, and also about the unpleasantness of cooking for one person. Anyway, I'm hoping to do something about the latter; it would be nice to get a small group of people together to eat meals every so often, if nothing else than to encourage us to cook more interesting meals. (If you are at Stanford and are interested in joining me, please do tell! This is especially true if you like vegan Indian food!) Since Wednesday, things have been better. We had an orientation for new math graduate students, so I was able to meet some of my classmates. The ones I have met so far are very nice people, some of whom have a surprising amount in common with me (which, I suppose, ought not to be too surprising given that I'm talking about a bunch of math graduate students). Yesterday was the algebra qual, which did not go well as far as getting correct solutions to questions, but it was fun anyway. It's been too long since I have done problems remotely similar to these, and it clearly shows. Evidently, then, taking the algebra course will be helpful for me. I'm really looking forward to my classes, which start on Monday. This post seems more content-free than I had planned on before I started writing it. Music: Boccherini La Clementina

	2007.09.04  09.38 Chess I played in the CalChess Labor Day tournament this past weekend, in the A section. I finished with 3.5/6: 3 wins, 2 losses, and 1 draw. I got the same score two years ago in the same section, even though I think I'm a much better player now. I was reasonably pleased with my first four games this time (1 loss and 3 wins, and I didn't play too badly in the loss), but my last two games left something to be desired. Here are three of my more interesting games (from rounds 2, 4, and 5): ( Round 2 ) I think I was well-disciplined in this game; I didn't need to rush my plans since his pieces were so tied down from an early stage. Therefore I was able to take time to stop any desperate counterattacks before they could get off the ground. ( Round 4 ) ( Round 5 ) My rating change is 1779-->1793. It's not what I had hoped for (breaking 1800), but it's something. I think my level of concentration was better than it has been in past chess tournaments, and I was more disciplined about calculating lines rather than playing somewhat intuitively. I still spent a considerable amount of time just staring blankly at the board, seeing what ideas would spontaneously make their way into my brain, but perhaps that's not a terrible thing. Music: Beethoven Songs

	2007.08.31  14.22 Scott Aaronson just posted the transcript from a very interesting talk he gave at Google a few weeks ago on his blog. He discusses various issues related to computational complexity, especially quantum computation and the ramifications of P=NP and why it would be a great surprise were it to be true. I find his claim about P=NP allowing the other six millenium problems to be solved by just doing a polynomial-time search through the possible proofs up to a certain length to be slightly suspicious (but only slightly, fortunately). Is there some way we could place a bound on the maximal possible length of the shortest proof of a given conjecture, should it be true? That seems to be very tricky, since some problems that can be stated fairly easily have very long proofs (for example, the four-color theorem). But I wonder if expressing the four-color theorem (just the statement, not the proof) in terms of ZFC formalism would actually require a large number of symbols. Still, a bound on the length of the shortest proof of a theorem requiring n characters to state seems very difficult to compute. It sounds faintly busy beaver-like. Mood: interested

	2007.08.24  13.18 Good decisions and bad decisions; possibly a self-indulgent ramble I think over the past year or so I have managed to make some good decisions in my life. Of course, I made good decisions before from time to time, but at least now I think I'm making fewer bad ones, so the net result is (more) positive. The first one was to become a vegetarian, almost exactly a year ago. I didn't plan on becoming a vegetarian seriously before, but it just suddenly occurred to me one day (August 30, 2006, to be precise) that it would be a good decision to stop eating meat. I was full of doubt about whether it was a good idea or not at first, but the good thing about such impulse decisions is that they tend to come with a large dose of initial motivation. And after the initial burst of motivation had been exhausted, I no longer consider going back to my old ways. I assumed that it would be difficult to stop eating meat, especially since I had eaten a lot of meat in the past, but I never found that I missed it. In fact, the food I've eaten in the past year has been more consistently good than ever before (at least if you discount the food I ate in the dining common) -- it's a lot easier to eat what I want when I cook it myself! I'm not a particularly good cook, but I enjoy cooking, and I can follow someone else's recipe if it's not incredibly complicated. Anyway, since I really enjoy food, and eating is an important part of my life (and probably just about everyone else's too), I think I became happier in general knowing that I was making better decisions regarding my food. I didn't expect that to happen, but it's a nice side effect. In fact, I've become more confident in my decision-making ability in general. People say I'm looking healthier than before too; that wasn't my goal, but it's another nice side effect. The problem is that my standards have gone up over the year, so now maybe I'm back to where I started, except that now I think I'm making bad decisions when I eat non-vegan food. I've been trying to do this less frequently, and eventually it will probably go down to zero, but I'm not used to making changes in installments, so it's difficult for me. Another good decision I've made is to become an atheist. Actually I don't know if ``become'' is the right word; I don't know if I would have said that I believe in god in the past, but I probably wouldn't have said I was an atheist. Actually I think everyone in my family is an atheist; my sister will admit it, but my parents want to redefine god to coincide with something they believe in. I tried that for a while, calling myself an ``axiomatic monotheist.'' (I just threw together popular scientific theories about the beginning of the universe and defined it as god.) But now I think that's not such a good idea. The point of having words is to be able to communicate with other people. (Well, maybe; as Orwell pointed out in 1984, it's difficult to have thoughts if you don't have words to describe them.) So if one redefines one's terms so they are inconsistent with the way other people wish to use them, then one fails to make use of a great advantage of language. It doesn't seem worth it for the sake of avoiding admitting to a controversial belief. It's really nice to be free of beliefs in silly and nonexistent things. And it's a bit easier to focus on leading a good life if you don't have to worry about what is/isn't going to happen after death. (Then again, I don't think I ever worried about that.) But it's easier for me when I am really confident in my beliefs. Tangentially related, I found this blog post on StumbleUpon today. It makes me hopeful that some kids can think like that. I suppose that it isn't exactly a good decision, but I will soon be living in my own apartment and taking care of myself. I'm really excited about not being looked after, although it's just a matter of degree. While I'm renting an apartment from Stanford, Stanford will be sort of looking after me, although less than my parents do and less than people at UCSB did. Anyway, it should be really enjoyable for me to take care of myself and be in charge of all my needs. Also, Stanford will be a new start for me. I have an opportunity to stop being pulled down by my bad decisions in the past. I am hopeful that I can get rid of some of them. Music: Beethoven Songs

	2007.08.09  12.52 So this is turning into a disaster: now they expect the flight from Vancouver to San Francisco that was supposed to leave at 1:03 to leave at 4:30. I will be really, really angry if I find out that the 11:30 flight from Vancouver to San Francisco wasn't full and that two people at Edmonton were lying to me when they said there was no earlier flight from Vancouver to San Francisco than the one on which I was booked. Mood: annoyed Music: Mozart Abduction from the Seraglio (in English)

	2007.08.09  11.18 Accidentally in Vancouver My direct flight to San Francisco was canceled, so now I'm in Vancouver for a rather lengthy layover. They told me that the flight yesterday from San Francisco to Edmonton didn't come, so they had to cancel the one today. Apparently they didn't think that it would be courteous to inform the passengers. (It wouldn't necessarily have helped me since I didn't check my email after about 3:45PM yesterday, but that's not the point.) Then I got on the flight to Vancouver, and we sat there for an hour when some 10-minute maintenance turned into a lot more. Anyway, I was pretty worried about figuring out how to contact my parents and get through customs in Vancouver before they left to pick me up, especially after the payphone failed to scan my credit card and I received something like seven answering machines or busy signals on collect, but eventually everything was successful. Then I found out that Vancouver airport has (a) orange juice and chocolate, my comfort foods, and (b) free wireless. So now I'm much more relaxed. I was pretty exhausted by the end of the workshop. I can handle a lot of talks if they aren't too hard, but it's incredibly draining to try to grasp something in one talk after another, day after day, when I lack sufficient preparation. There were a bunch of talks that I understood well, and a number of others that I was able to understand partially, but then there were plenty that lost me nearly immediately. I guess it makes sense that I shouldn't understand everything when most of the participants were more experienced. Anyway, I definitely got a lot out of the summer school, and I'm really glad I went. Mood: relieved Music: Mozart Abduction from the Seraglio (in English)

	2007.08.03  07.11 Hello from Edmonton, and paper success So I'm in Edmonton for the PIMS Algebra Summer School. It's a lot of fun, and I'm even understanding many of the talks! I'll report on some of the more interesting ones (probably on Wordpress) when I get back, but my main impression for now is that Galois cohomology is of the utmost importance, and I have no business not understanding it really well. Also, the paper Jeff and I wrote was accepted to CAOT, volume 1, issue 4. The referee's report is extremely positive. Yay! Mood: pleased

	2007.07.20  09.41 Checkers Checkers has now been solved. After an 18-year computation, it has been concluded that checkers is a draw. At the same rate of computation, it would take well over 10^20 years to solve chess. Music: Bruch Scottish Fantasy

	2007.07.01  12.42 'Vantage Number One (of Not Throwing Things Away) Usually that's a fairly bad habit that plagues me, but on this particular occasion I happened to want to read an article from a Time issue from 1999. That's easy! It happened to be at the top of a drawer in my filing cabinet, and I found it only seconds after I realized I wanted to read it. Music: Gade Octet

	2007.06.29  15.23 Apparently I'm not alone A year and a half ago I posted a letter that I sent to the registrar of UCSB stating that it was not appropriate for move-in weekend to be the same weekend as high holidays. Today an article appeared in the Jewish Bulletin stating that the University of California will avoid such conflicts in the future. I am very pleased that others feel strongly about this issue and that the University of California has made an excellent decision. Mood: pleased Music: CPE Bach Cello Concerto #2

	2007.06.14  19.26 And with one final email that I sent off seconds ago, I am now completely finished with my career as an undergraduate. Yesterday I asked Agboola for some recommendations of papers to read in preparation for AIM's workshop on the Tate Conjecture. He recommended two papers of Ramakrishnan; I started reading one of them (``Regulators, Algebraic Cycles, and Values of $L$-functions'' in Algebraic $K$-Theory and Algebraic Number Theory,...), and it's completely terrifying! Yesterday I got through the first section without too much trouble, but then in the second section he immediately started discussing group homology/cohomology and $K$-theory. So this morning I taught myself enough about group homology to understand four lines of the second section. (That amounted to convincing myself that $H_1(GL_n(\mathfrak{o}_F),\mathbb{Z})\cong\mathfrak{o}_F^\times$.) After that it appears hopeless, at least for the remainder of section 2. Then I tried section 3. I fared somewhat better, making it through nearly a page, but I really need to learn more about Artin $L$-functions. But that should be easier than this continuous cohomology and $K$-groups in section 2. The other sections seem far, far above my head, and I don't know where to start on them. I really want to understand something at the workshop though. But at the moment, I can't even understand the statement of the conjecture. Music: Corelli Concerto Grosso #10

	2007.06.11  15.31 Am I a graduate student now? I graduated yesterday. It doesn't seem like a particularly big deal to me, I suppose primarily because I never doubted that it would happen. But it was nice, and my parents and grandparents came to see it. Apparently the speeches were pretty good, although they were more or less inaudible on the stage. Anyway, I am now in my last few days at UCSB. Hooray! Music: Haydn D Major Cello Concerto

	2007.05.31  12.05 The ABC Theorem!?!?!? Apparently Szpiro has a proof of at least certain cases of the ABC conjecture. (He was able to find an explicit constant K(epsilon) for certain values of epsilon.) His bound is good enough to prove Fermat's Last Theorem for n>81 (which is presumably good enough to combine with pre-Wiles results for a full proof). And the proof is actually supposed to be understandable to a person like me. Mood: surprised Music: Debussy Prelude to the Afternoon of a Faun

	2007.05.19  18.24 So I guess a few things happened to me recently. I will not be a recipient of the Chancellor's Award for Excellence in Undergraduate Research at UCSB this year. This doesn't surprise me. I consider the research that I have done so far to be rather low-quality; certainly I was capable of doing much more and much better research, and probably without giving up very much other stuff that I did as an undergraduate except possibly playing solitaire. I think the math department nominated me for it because I had done a bit of research, and they didn't really have anyone else they could think of. (But they deny this of course!) The professors think I didn't get it because a math student got it last year, and they don't want to give it to the same department too frequently. But the other problem for me is that I'm a terrible salesman. It's difficult to try to convince other people that I am intelligent or am deserving of awards when I do not believe it myself! Anyway, the math department is giving me one of their own awards (Raymond L. Wilder Award). I suppose I deserve that one since I certainly believe that I have worked much harder than any other math major here. I also had the pleasure of completely failing the last exam I will take as an undergraduate (in my quantum computing class). Actually the last sentence is a lie; it was not a pleasurable experience at all. Apparently this professor has a habit of giving very challenging exams, but I didn't know that (having never taken a course from him in the past). It does feel strange that I believe that I understand what we discuss in class, that I can make meaningful contributions to the lectures, and I can solve the problems he posted on the website, but yet I was not able to demonstrate a satisfactory level of knowledge on the exam. I guess recently I have been spoiled by exams in which I can easily answer everything (or nearly everything) confidently once I have mastered the subject matter. I keep getting roped into giving talks this quarter, so I have four of them to give next week. Two are in combinatorial game theory (as usual); I'll talk about games with entailed moves and then some stuff with infinite games and ordinals and surreal numbers unless I suddenly come up with a much better idea. Then I have a talk in the analysis class on the prime number theorem (go figure!), and then I should give one in cryptography on something in elementary number theory, possibly but not necessarily related to cryptography. Right now I'm thinking about doing quadratic Gauss sums, but that could change if I suddenly get a better idea. Today I watched two of Conway's videos, one of which played a large part in preventing me from getting as much work done as I would have liked. The aforementioned video was on lexicographic codes (lexicodes). You can watch it following the link from here, but I suggest you not do so if you have work you need to get done! After watching it, I tried surfing around on the web for more information about lexicodes, with minimal success, and then headed over to the library to look at Conway and Sloane's book on some related topics, and again I was not pleased with the lack of information on lexicodes. After that, I headed over to CCS and managed to find a paper the two of them wrote on the subject. I then tried, as a test, to give the same lecture that Conway gave in the video on my own (sans anecdotes, but including the gimmicks with lexicode theorem/non-theorem/very non-theorem), without any notes, and I found I had no difficulty in doing so. This stuff isn't really appropriate for the CGT class, but I might check if there are any slots open in the discrete geometry seminar for me to give a talk like this; I'd fill the rest of the time up with cool stuff about nim and nim fields; it is hoped that I will get a better reception in such a seminar than I did in my class. Now I ought to go to a location free of computers to prepare my talk on the prime number theorem. Mood: excited