Saturday, July 8th, 2006
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1:42 pm - Bill Mayer on Intelligent Design
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Wednesday, June 14th, 2006
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1:59 pm - Chords are Dead
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Sunday, June 4th, 2006
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2:38 pm - POKER!
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I've started playing a lot of poker. Like, 5 nights a week. I'm also kind of bad about inviting people from outside the house, mainly because I can usually find 5 people to play on a moment's notice here...
So if like no-limit hold'em and want to be occasionally invited to play, respond to this post and I'll call you next time we play.
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Friday, June 2nd, 2006
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4:11 pm - Betcha can't post just once (Bill o reilly)
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4:11 pm - John Stallings on ethics:
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John Stallings on ethics:
"Authority is not that meaningful. People, humans, individuals, these are important. There are many people who are healthy and looking forward to things like Art and Music and Mathematics, as well as good food and achievements and friends. No pain will stop a reasonable person from enjoying life first. Deal with it now. Learn from the bad experiences of life, but don't let that stop you from having good experiences too. Get that piano tuned. Grow some wild flowers. Sneak into a symphony performance. Breathe that good air and run and let the sun shine. Help your close friends, but don't worry about everybody. Let others worry about you instead. Disgust people, shock them, have a good laugh."
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3:53 pm - Serre, semi-stable reduction and split torsion
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I'm going to start blogging any interesting statements I come across in papers that I don't have time to follow up on.
For example:
In "Propriétés galoisiennes des points d’ordre fini des courbes elliptiques." Invent. math. 15, 259–331 (1972), Serre proves that if E is a semi-stable elliptic curve (i.e. good or multiplicative reduction at all primes, or equivalently its conductor is square-free) and E -> E' is a p-isogeny over a field K, then E or E' has a point of order p defined over K.
I have no idea why this should be true. In concrete cases its not even that important to me, because you can always quickly check things like torsion subgroups.
This is important to me because I have a trick to solve fermat equations of signature (2,3,p), using elliptic curves of conductor p (hence semistable), but my trick involves explicitly finding a 2-saturated subgroup of the mordell weil group. Having a p-torsion point, or even better, split torsion, makes descent (which is the only way we really know how to solve ellitpic curves) a lot cleaner.
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Monday, April 24th, 2006
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5:14 pm - Starsky and Hutch
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We Americans are the only ones who didn't get creamed at some point during all of this. We are free and prosperous because we have inherited political and values systems fabricated by a particular set of eighteenth-century intellectuals who happened to get it right. But we have lost touch with those intellectuals, and with anything like intellectualism, even to the point of not reading books any more, though we are literate. We seem much more comfortable with propagating those values to future generations nonverbally, through a process of being steeped in media. Apparently this actually works to some degree, for police in many lands are now complaining that local arrestees are insisting on having their Miranda rights read to them, just like perps in American TV cop shows. When it's explained to them that they are in a different country, where those rights do not exist, they become outraged. Starsky and Hutch reruns, dubbed into diverse languages, may turn out, in the long run, to be a greater force for human rights than the Declaration of Independence.
( Read more... )
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Tuesday, April 18th, 2006
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10:12 am - Pari
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Help!
I'd like to install Pari on my home computer with as little pain as possible. How should I do this? I'm running Mac OS X.
Thanks!
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Monday, April 10th, 2006
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10:17 pm
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A mathematician named Klein
Thought the Möbius strip was divine.
Said he: "If you glue
The edges of two
You'll get a weird bottle like mine!"
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Friday, March 3rd, 2006
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7:44 pm - Strong Torsion Conjecture
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To me, "recent" means "in the last couple of years". But apparently in mathematics "recent" means "in the last twenty years".
Apparently, an effective version of the Strong Torsion Conjecture was proved, as "recently" as 1999. I find this interesting because no one I've talked to was sure if the Strong Torsion Conjecture had been proved at all, and the ones who did said it was highly unlikely that there was or would soon be an effective version.
Let E be an elliptic curve, and let K be a number field over Q of degree m. The then if E has a $p^n$ torsion point, $p^n \leq 129(5^m - 1)(3m)^6$ and $p \leq (1+3^{m/1})^2$. This result is circa 1996, or maybe earlier, and uses Falting's Theorem and a very deep theorem of analytic number theory.
A much celebrated version of this is Mazur's theorem, which is the strong torsion conjecture for m=1, i.e. elliptic curves over Q. It is effective, I would even say very effective: The only torsion subgroup of elliptic curves over Q are Z/NZ for N=1..10 or 12 or Z/2Z \times Z/2Z. This result is circa 1977 and uses some Hardcore Algebraic Geometry. Really, you don't want to run into this proof in a mosh pit. Its THAT hardcore.
A similar sharp result is known for m = 2 (i.e. quadratic fields), due to Kamienny, as recent as 1992. As far as I can tell, there are no similar sharp results for other m.
I was hoping that a sharp enough bound for these would solve my thesis problem, but no dice.
Alice? Who the fuck is Alice?!? (Sorry, figured I should add something to amuse Jesse in this post).
This is Alice: www.math.uci.edu/~asilverb/bibliography/pcmibook.ps
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Sunday, February 26th, 2006
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11:41 pm - T-Rex: Bread
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you might question choosing humble bread as a favorite food, but next time you're eating it, consider how good it is, and how we've had like three thousand years to perfect it. imagine what pizza will be like in three thousand years. that's what bread is like RIGHT NOW!
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5:23 pm - Emacs Question
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I'm learning to use Emacs.
Question: What is the meta key on the new powerbooks? And yes, I know I can use Esc, but 1) that's different than the meta key and 2) its small and in the corner, so it doesn't really speed things up.
UPDATE: Terminal menu -> Window Settings... -> Keyboard
Then select `use opt as meta'.
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3:37 pm - Computing Questions
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1) Dear Berkeley Math people: Do you know how to use MathSciNet from home?
2) Is there any way to Save just part of a PDF?
3) From a command line, is there any way to print a specified number of pages?
Thanks!
EDIT: http://proxy.lib.berkeley.edu/configure.calnet.html#safari solves #1 (Thanks to Paul for suggesting the use of a proxy and Tony for showing me how).
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Monday, February 20th, 2006
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12:20 am - The low-down
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This week's contribution to the blogging world are the following three pictures:
And this too!
Photoblog!
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Tuesday, January 24th, 2006
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2:02 am - Overheard at MSRI
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[referring to Hartshorne vs EGA]
"Why read a good book by a good mathematician when you can read a great book by a great mathematician?"
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Monday, January 23rd, 2006
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12:59 am - Books and Music
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I'll have my external hard drive with lots of music/books in my office for most of this week, so please stop by Evans 712 and trade electronic stuff with me!
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Wednesday, January 18th, 2006
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11:47 pm - The OMD QOTD
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"I wish you were my GSI. Because then you could teach me linear algebra and afterwards we could get dirty."
*she reads this as I'm writing it and says*
"Ah! And then we could Couple!"
current mood:  hot
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Thursday, December 29th, 2005
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7:47 pm - Research Statement
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I decided to solicit more money from the government and throw together an NDSEG application. Here's a draft of my research statement. Most of the time writing it was spent trying to reduce it to less than 3000 characters...
( Tantalizing Questions )
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Sunday, December 18th, 2005
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5:53 pm - West Coast Number Theory Conference Day 3($\empty$)
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The Rain: This picture will likely say enough.
Comparison: David Jordan gave me a problem recently about counting points of bounded height in the cantor set. Due to a random conversation with a speaker after a mostly unrelated talk, I think I have solved it. This is one of those nice things that I've always hoped would come of talks - helping to put pieces of random conversations together to create some piece of mathematics.
Also compare this to most other talks I go to, where I don't have too many questions other than "what does that word mean". Well, I've gotten a lot out of asking that question, but this conference has been nice in that I seem to have more questions with content to ask people than I have time to ask them. Which is nice.
I don't really feel like blogging much today: So instead I'll follow suit and put up this awesome picture of the OMD, for those of you who haven't had a chance to meet her yet. There's also some new picts up on my website if you're craving more.
I'm going to go to dinner now and try to find a bit of cell phone reception.
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5:42 pm - West Coast Number Theory 2 (This subtitle is about how I think its funny to
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Today was good. I was less shy today.
Brillhart: Highlight of the morning: John Brillhart sat down next to me at the end of breakfast. He didn't seem to remember me. After a day we're getting along pretty famously.
I mention that I took his linear algebra course. His response? And you're still around doing math?!? He says "hi" to Santiago and Joshua, and also has adopted me as someone to hang out with and tell Paul Erdos stories to.
Nils: We're getting along well too. This is the second conference where I've snapped a good picture of him sleeping in a talk.
He sits down next to me at lunch, evil grin handy, and says "I'm starting to recall the Bremen conference a little better." I.e. he remembered the midnight sumo-wrestling.
Grad Students: I am one of 3-7 grad students (some of them might be post docs). Logic and number theory came up, and I managed to give a complete proof of Hilbert's 10th modulo the diophantine-listability equivalence plus the construction of the magic prime spitting polynomial, on the spot, on a single sheet of paper.
I hope this means I'm turning into Bjorn.
Campfire Stories: I'm currently sitting around the fireplace with a couple of middle-aged mathematicians, listening to them tell silly drunken stories.
For instance, B is telling a story about someone in the town he grew up in poking holes in all of the condoms in the one store's corner store. He then makes the correlation that five years later the incoming kindergarden class was 3 times the size.
Also a fun fact of the day: If you hit a cow with a car it rolls and damages the entire car. As opposed to a dog, which doesn't roll and just just tears up the front.
Talks: The talks have been fun and entirely comprehensible. There were two really interesting ones: one about criterion for decomposing Jacobians of curves into products of elliptic curves and the other (Nils!) about obstructions to rational points on "Wee" hyperelliptic curves of genus 2. Read the last line in the context of the subtitle. You're going to hear that one a lot next semester.
The rest of the talks were more elementary and a source of fun distracting problems.
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