Ramblings of a Pissed Off Mathematician
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dhilbert83's LiveJournal:
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Saturday, July 28th, 2007  11:36 pm 
R.I.P. Dr Wisewell. You Will Always Be Remembered.
I didn't know you for that long, and I so wished I had gotten to know you better, but as a fellow mathematician who worked in your field (analysis), and as someone who opened up to me beyond the professional realm, I felt an uncommon bond between us. It absolutely made me smile when you said that I should come visit the Uni of Glasgow math dept., and I was really looking foward to finally meeting you (along with Robert and his advisor Dr. Pott) in person next year in Toronto (at a harmonic analysis conference.) I'm just still in shock and can't believe it.. I always looked up to you since I felt that you were a moral, gentle, and caring professional mathematician (who had infinitely higher potential than I do) who was able to fight your demons and win , but I never ever imagined that they would triumph in the end. I just wish I checked LJ more often so I could have read when something was wrong and said something, or been in your math dept. so I could have noticed when you didn't show up for work, and try to beg you to stay strong for just a little longer and promise you that we all, friends, family, and doctors, would help you find a way out of this, a way that YOU would be comfortable with. It just didn't have to end this way. I just can't believe.. But if there is a god, then I know he'll understand what pain you went through and give you a well deserved spot in heaven. Rest in peace my friend. You and your work will always be remembered. Dr Laura Wisewell  Tuesday, June 27th, 2006  9:53 pm 
So after 6 hours or so, I gave up :p. Conway's 'course in functional analysis' has the same problem (show that L^\infty, for various probability measures, are the only abelian Von Neumann algebras, up to isomorphsim), but refers to previous problems for hints, and so I gave up and looked at the hints. Still haven't solved it WITH the hints yet. In other news, more fun craziness in the middle east (what the hell else is new hah). I hope Israel agrees to some prisoner exchange thing. Invading Gaza can't help things in the least bit. Oh well, off to try to get this damn problem solved, so I don't have to feel like shit tommorow (and so I can move on in my work) :). Oh yea, I absolutely love this song. This is definately best MDB song I've heard, apart from the 'Turn Loose the Swans' version of Sear Me. Oh while I'm here... Now I usually like 'moveon.org' (I hope Denise isn't reading this hah!) but this is kind of dumb "We need to seize this moment to make sure the media and the public know that the Republican addiction to oil money is keeping gas prices high and holding America back from the clean energy future that we desperately need." How in sam hell is HIGH GAS PRICES holding American BACK from clean energy? High gas prices has caused a huge increase in low milage cars (albeit, mostly foreign cars, but whose fault is that? that Detroit didn't put out good low milage cars). Sooner or later, gas will run out, and high gas prices are needed for us to consume less gas. Yes, this hurts the poor much more than anyone else, but then the govt. should step in somehow to help this. Anyway, enough for tonight :). Off I go to work.  9:05 am 
Damn thing didn't work before, so here it is:  9:01 am 
This brought a smile to my face this morning :). Anyway back to operator theory. I hope this HW problem (proving abelian W* algebras are all isomorphic to some L^\infty) won't take me all day. Of course, I'm sure it will. But hey, how else am I to learn if I don't do the problems I guess?  Sunday, June 18th, 2006  10:31 pm 
Well I'll be damned, a publishing company just recently translated one of my favorite books "Hitler's Priestess" into Italian. I guess now Italians can learn about the bizzare (and completely politically irrelevant) lunatic known as Savitri Devi :). I guess I take people like her too jokingly and lighthearted, but how can someone not be morbidly curious about a woman who makes (or rather 'made' as she died in the early 1980's) Ann Coulter look like a pinko liberal wussy :p  7:25 am 
This is the dumbest little problem I have. It's really just second year Undergrad linear algebra, but seemed to trick me up last night. So my dog woke me up at 6:45am, took him out, fiddled online, so now I'm pissed and must solve this now :p. T is self adjoint iff [ Error: Irreparable invalid markup ('<tx,>') in entry. Owner must fix manually. Raw contents below.] This is the dumbest little problem I have. It's really just second year Undergrad linear algebra, but seemed to trick me up last night. So my dog woke me up at 6:45am, took him out, fiddled online, so now I'm pissed and must solve this now :p.
T is self adjoint iff <Tx, x> is real for all x in H (H some hilbert space, but the proof is probably exactly the same for matricies on euclidean N space). My book says 'use polarization' and so I'll try that again. I hope this doesn't take to long cause I want to go running soon.  Wednesday, June 14th, 2006  8:07 pm 
You know, one of these days when I'm bored, I'm going to make a gigantic list of every single function space (vector spaces of functions) I've ever heard of. Considering the fact that I've seen a lot of 'regularity spaces' (in a miserably failed attempt to come up with a new Sobolev type compactness imbedding), a lot functions spaces that arise in a more banach space theory setting (for my Lp compactness research, though I couldn't even understand the definition of most of these spaces at the time, and probably still can't hah), and now a lot of Banach spaces of Analytic functions via my studying operator theory now (I guess I wouldn't count noncommutative functions spaces since they really aren't function spaces). I find it hilarious just to think of how many dozens of dozens of spaces I can come up with. God I love analysis :).  Tuesday, June 13th, 2006  11:52 pm 
Children, play nice...
God I love this: Hamas, the leading group in the Palestinian government, claims to be obeying a 'cease fire' while for months, have been firing dozens of homemade (qassam) rockets into Israel (usually resulting in no damage, though it somestimes does kill or wound Israelis.) Now that's one hell of an interesting cease fire. A shell recently blows up on a Palestinian beach, killing a family of 7 civilians. Human Rights Watch and others claim it was an Israeli shell and initially Israel officially even expressed regret for the incident and stopped shelling in response. However, after an entire day long investigation (what length!), Israel now claims it could not have been an Israeli shell, despite the fact that Israel was shelling 250 meters away from the where the family was beaching, and thus in the end, there doesn't appear to be a straight story as to where this shell magically came from. (Now why would a family attempt to enjoy a nice day on the beach while areas 250 meters away are being shelled is a little strange to me...) Hamas declares that the 'cease fire' is no longer in effect (thus, most likely, there will be government sanctioned suicide bombers attacking Israel.) Israel decides all of a sudden to target airstrikes at two Palestinian militants (men from Islamic Jihad). They get their targets, but kill 7 civilians, including two children, and wound nearly 30 civilians in the process. Oh, and in the meantime, the two major political factions in Palestine, Hamas and Fatah, are busy having fun with each other (or rather engaging in constant gun battles with each other, and the occaisonal setting of the prime minister's office on fire http://news.bbc.co.uk/1/hi/world/middle_east/5073548.stm ) on a daily basis via a power struggle that started ever since Hamas won elections. It just can't get better than all this. Oh wait, it does: the Palestinian government, with the EU and USA withholding funds until Hamas actually acknowledges that there exists a country called Israel, is so bankrupt that it can't even pay most of it's own government employees.  10:14 am 
"ruled by the supreme court that states can ban cross burning if the intent is racial intimidation" obviously I meant CAN'T instead of can hah.  12:30 am 
grrrr
This pisses me off: "We punish people for painting a swastika on a building, and we punish people for cross burning. Some might claim that's free speech, too. I think not," This is said by my (well not mine anymore since I'm a NY resident, but I'm still a NJer by heart heh) senator, sen. Menendez. This dumbass should actually look into why it was deemed illegal to burn crosses: it was very recently ( http://www.cnn.com/2003/LAW/04/07/scotus.cross.burning/index.html) ruled by the supreme court that states can ban cross burning if the intent is racial intimidation (since according to them, this is more akin to a violent threat, given the history of the KKK, rather than anything to do with free speech). But that all cross burnings can not be considered on its face intimidation. Anyway the point is, what the hell does the former two have to do with the latter? You punish people for cross burning because it's a clear violent threat a lot of the time. How is flag burning intimidation? Now I'm a liberal a lot of the time, but I'm a 100% liberterian on this issue. I don't want to see this country turn into most European countries, where you can go to jail for 'offensive' speech. Granted it's different for them, since some european countries often 'flirt' with extreme right views (ie Austria with Jörg Haider, Le Pen and france, germany and the NPD, or just the antiimmigration sentiment in a lot of countries .) But still, any weakening of free speech is a slippery slope. If the 'right wing' gets a flag burning amendment today, then possibly tommorow the 'left wing' will get some other antifree speech tommorow, and so on... Anyway, just was doing some browsing, and this is one HELL of a quote by Haider in dec. 1995 ( http://news.bbc.co.uk/1/hi/world/europe/628282.stm): "The Waffen SS was a part of the Wehrmacht (German military) and hence it deserves all the honour and respect of the army in public life." That's pretty fucked up. It's members being forced to join or not, that's like praising the NKVD, KGB, or Stasi, especially given the reputation of most Waffen SS units. At least he didn't praise the Einsatzgruppen I guess :p. Oh well, I have operator theory to do tommorow, and I get to read up on the Bergman and pseudohyperbolic metric on the unit disk, fun :). Hopefully in not too long, I will be able to read some papers on Toeplitz and Hankel operators on domains in Bergman space.  Saturday, June 3rd, 2006  12:01 am 
One last thing: I find it kind of funny that for the whole week, I've been doing harmonic analysis and didn't even know it!! Apparently a functional analytic/measure theoretic study of harmonic functions is considered harmonic analysis :).  Friday, June 2nd, 2006  11:49 pm 
Also, I'm totally stuck on one of the Rudin problems: finding conditions where one invariant subspace of the shift is propery contained in another. I'll try tommorow again.  11:10 pm 
So today I got through quite an elegent result in math: Beurling's theorem. It completely characterizes the invariant subspace of the unilaterial shift on l_2. The idea is to switch from l_2 to H^2 (the Hardy space) and so using Hardy space theory, these subspaces are completely determined by (and to each combination one can associate an invariant subspace to): a sequence of complex numbers a_n where lim a_n = 1 and sum (1a_n) converges, and a finite Borel measure on the circle that's singular with respect to Lebesgue measure. Nice thing is that it's very conceptual and not hard at all (I'm using the complex analysis part of 'Adult Rudin.') The thing is though, I have to wonder: why should I, or anyone for that matter, even care about invariant subspaces of the shift? Is the shift operator at all useful? Or do people do this stuff for the hell of it? Who knows...  Wednesday, May 31st, 2006  8:20 pm 
God do I love my friends :) (nilsan isn't the person's full nickname on AIM.) DHilbert83: anyway yea I used to care about politics a lot more than I do now Nilsan: thats good... Nilsan: politics = grey hair Nilsan: just look at our house of reps. DHilbert83: hah DHilbert83: hah unfortunately you might have to get your hands dirty with some of the political crap, if your an intel analyst Nilsan: ja... Im already into that Nilsan: the fucking free masons dominate this brigade Nilsan: cocksuckers... DHilbert83: hah Nilsan: they couldnt run a squad.... forget a brigade Nilsan: I would run this BDE so much better... Nilsan: /stares down at rank Nilsan: oh well Nilsan: gimi like Nilsan: 5 years DHilbert83: I sure as hell wouldn't so I can't really say much DHilbert83: hell, maybe you can climb the ranks DHilbert83: :) Nilsan: ya.... intel analysts climb rank fast Nilsan: and i already know shit sergants should know so Nilsan: im set for any board that comes up  Saturday, May 27th, 2006  10:15 am 
This just made my day. :)  Thursday, May 25th, 2006  12:15 am 
You know, I have to admit that the complex analysis I'm studying (Hardy Space/Bergman Space theory) is absolutely amazing. It's a beautiful combination of functional analysis (basic hilbert/banach space theory, basic function spaces and their duals, etc), measure theory (borel measures on the unit circle, differentiation of complex measures, etc), and of course, complex analysis. And I haven't even gotten to any of the non trivial operator theory part :). Anyway, seems like Hamas and Fatah are at it again. Do I smell civil war in Palestine? Doubt it. Fatah definately wouldn't want civil war, and I really don't think Hamas is dumb enough to want it either. Then again, both the Israelis and the Palestinians have the rationality (and too often the morality) of a two year old, so I guess it shouldn't surprise me if civil war breaks out. The sad thing is if it happens, the Palestians will be even more economically devistated, which is hard to fathom since they currently have the LOWEST GDP of any country (well there is no 'palestine' but as a people) in the world (besides I think Haiti lol.) Anyway, the Israelis and Palestinians are so far apart politically that any sort of 'we won't murder each other' type of deal (like what the Protestants and Catholics recently made in Ireland) won't happen for, at least, 510 years I guess, if it ever happens which sucks the conflict fuels worldwide antisemitism, and on a personal level, my cousin (I have family in Israel) was once one bus away from getting blow to smitherines (ie if he had taken the next bus, he would be dead.) But that's life I guess ... Now, off to sleep I go and onto math tommorow :). Current Mood: calm  Sunday, May 14th, 2006  8:10 pm 
Interesting
I remember watching Black Hawk Down (one of my fav movies) and listening to some of its music. A portion of the music had a VERY distinct sound similar to old Dead Can Dance, and well what do you know, turns out Lisa Gerrard (of DCD fame) did some of the music.  Monday, May 1st, 2006  11:19 pm 
Think I got it
I think actually, the direct sum of a shift and a unitary operator is another shift plus a rankone operator (which is of course compact.) Of course it's almost trivial to prove this it seems. I'll recheck it tommorow. Anyway, not sure what I'll study this summer. I can either try to get through the first two chapter of Davidson's "C* algebras by examples" (no fucking WAY i'm touching chap. 3 on AF algebras yet. Though it would be awesome to get through Elliot's classification of AF algebras via elementary Ktheory). Or try to get through a few chapters of Zhu's book on Bergmann Spaces. The latter has the advantage that it'll be not much harder to read, AND the oldest result in the ENTIRE book is from like 1960 lol. And after the first chapter, nearly the WHOLE book is results from 1990 and afterwards. Yet with the former, I'll learn whether I was an idiot to even think I would ever do operator algebra research. Even then though, the first two chapters (on banach algebra basics, C* algebra basics, C* algebras of compact operators, Abelian C* algebras, and whatnot) do not even TOUCH 'modern' approaches to C* algebra, so even if I like it, shit like BDF theory or Ktheory could utterly whip my ass. Then again, I almost admire these wackjobs who try to turn everything in math into 'noncommutative' stuff. I've even seen people propose noncommutative analogues of Sobolev Spaces, or PDEs themselves!!! Current Mood: blah  Thursday, April 27th, 2006  11:38 pm 
Anyway
Anyway I'm going to ramble about how I'm pissed that Uni of Pitts didn't give me support. HOW THE FUCK DID THIS HAPPEN!!! After reading my paper, one of the professors (chris lennard )literally solicited me to be his advisee. Yet I was put on the shortlist, and apparently not high up on the list. Meh. And it appears that my paper is utterly worthless for PDE sake (ie evolution equations or abstract ODEs in Banach Spaces.) I think only the Banach Space theorists (these are the people who still give two shits about research in Lp spaces, since, obviously, Lp is the utmost classical Banach Space there is, and so is a nice model for isomorphism theorems I guess?) would give two shits about the paper. And lets be frank here..., except for a few guys at Kent state, some guys down in Texas (like hell I'd ever go down to TX and do a postdoc lol), and a few others scattered around the country, who the hell does Banach space theory in the USA?!? There are current results that are useful elsewhere (for example, a professor here at Buffalo, who does noncommutative dynamics, used Rosenthal's "l1 theorem" in a very nontrivial way) but it seems that unless you do something 'grandspanking,' is anyone going to care? This is especially irking since Banach Space theory has the reputation of being terribly difficult. I guess function theoretic operator theory isn't much different (which is what I may end up doing). A guy here who just finished his thesis in that, admitted to me that he has no clue what the hell is work is even remotely useful for, and neither does his adviser (who is a decently well known operator theorist Jingbo Xia). Difference is, people DO seem to care about operator theory, and there are a lot of operator theorists in the USA. Anyway I FINALLY learned what the HELL a 'reproducing kernel' is. And it makes sense :) if yo uhave some function space H (a hilbert space), and point evaluation z(f) = f(z) is a continuous linear functional, then by Riesz theorem (fix z), this is given by z(f) = f(z) = [ Error: Irreparable invalid markup ('<f,>') in entry. Owner must fix manually. Raw contents below.] Anyway I'm going to ramble about how I'm pissed that Uni of Pitts didn't give me support. HOW THE FUCK DID THIS HAPPEN!!! After reading my paper, one of the professors (chris lennard )literally solicited me to be his advisee. Yet I was put on the shortlist, and apparently not high up on the list. Meh.
And it appears that my paper is utterly worthless for PDE sake (ie evolution equations or abstract ODEs in Banach Spaces.) I think only the Banach Space theorists (these are the people who still give two shits about research in Lp spaces, since, obviously, Lp is the utmost classical Banach Space there is, and so is a nice model for isomorphism theorems I guess?) would give two shits about the paper.
And lets be frank here..., except for a few guys at Kent state, some guys down in Texas (like hell I'd ever go down to TX and do a postdoc lol), and a few others scattered around the country, who the hell does Banach space theory in the USA?!? There are current results that are useful elsewhere (for example, a professor here at Buffalo, who does noncommutative dynamics, used Rosenthal's "l1 theorem" in a very nontrivial way) but it seems that unless you do something 'grandspanking,' is anyone going to care? This is especially irking since Banach Space theory has the reputation of being terribly difficult.
I guess function theoretic operator theory isn't much different (which is what I may end up doing). A guy here who just finished his thesis in that, admitted to me that he has no clue what the hell is work is even remotely useful for, and neither does his adviser (who is a decently well known operator theorist Jingbo Xia).
Difference is, people DO seem to care about operator theory, and there are a lot of operator theorists in the USA.
Anyway I FINALLY learned what the HELL a 'reproducing kernel' is. And it makes sense :) if yo uhave some function space H (a hilbert space), and point evaluation z(f) = f(z) is a continuous linear functional, then by Riesz theorem (fix z), this is given by z(f) = f(z) = <f, K_z> for some K_z in H. So as we usually take some subspace of L^2(C^n) or something like that, this K_z is a kernel.
Also, for n = 1, if H consists of holomorphic functions it's standard that L^2 convergence implies L^infty so in fact point evaluation Is continuous.
As always, this is probably not at ALL easy for n > 1, as nearly all function theory/operator theory gets hairy if n > 1/
So yea. I'll state my summer plans soon. In short, I'm going to try to read some of Kehe Zhu's (a SUNY Buffalo graduate!!!) SpringerGTM book on recent progress in Bergmann space theory. I don't know if I have enough function theory backround, but I'll try. They do a section on the Berezin transform, and so maybe I can read some of the very recent reserach papers of a professor here on that subject.
Good shit :)
On a last note, these three talks by Arveson may have scared me into doing anything algebraic, ie operator algebras. We'll see how algebra goes next year though. Current Mood: exhausted  11:28 pm 
Past Three Days
So, for the last three days we (SUNY Buffalo) have had one hour talks by Bill Arveson. Two of them are on the utterly bizzare intersection of operator theory and algebraic geometry/commutative algebra. Needless to say, I understood nothing lol. The second, which was more accessible to me, was on the state of noncommutative dynamics. He said something that I should be able to solve (I think lol): "If you have the direct sum of unilaterial shifts on a separable hilbert space, then this is a compact perturbation of a unilaterial shift (ie S + K where S is a shift and K is compact.)" Any ideas ? Maybe he meant 'this is unitarily equivalent to...'? :p Current Mood: drained 
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