after attending the joint mathematics meetings in san francisco, i want to share two points you should not try to copy when you’re organizing a conference.

• in case you have a lot of parallel sessions, try to schedule sessions with similar topics in parallel. this minimizes the number of days people from these areas have to attend the conference.
• promise wireless internet, but do not provide a backbone which can handle this. after noticing it is too slow, simply turn it off for the rest of the conference.
• this applies more to conference center owners. do not install power plugs anywhere near to areas where tables and seats are placed. and by any means, never install power plugs in rooms where talks are held.

people will really appreciate this and regard your conference as one of the best ever.

the last two weeks were pretty much packed with two conferences and a summer school. on august 13–14, i.e. thursday and friday, the selected areas of cryptography conference was held in calgary. then, the week after that, the ecc summer school was held from wednesday to saturday, and from sunday afternoon to wednesday the 13th workshop on elliptic curve cryptography was held. (in fact, this was the sixth ecc workshop i attended, beginning with the one 2004 in bochum. and the second ecc mentioned in this blog; apparently i was too busy to write something about the 12th one held in utrecht last year.)
in addition to these things, several more things happened, some about whom i might write a few words in some more posts.

as you may have noticed, i use wikipedia a lot – both for linking to descriptions of terms i use in this blog, and for looking up stuff myself which i encounter somewhere, may it be offline or online. usually, chances are good that wikipedia offers at least some kind of description which answers my questions, or at least helps me getting an idea. but from time to time, it happens that you try to look something up on wikipedia, only to find out that such an article existed but was deleted – for example, because it was “not relevant”. i can understand that people do not want to see wikipedia flooded by biographies of john doe and jane roe – only a handful people are interested in these, probably most notably john doe and jane roe themselves.
but there are cases where i simply can’t understand the decision. for example, there is the chilenian doom metal band mar de grises, which i discovered by chance in zurich’s now deceased knochenhaus. according to the wikipedia deletion log, it is “not noteable” and failes some guidelines. so, who decides what is noteable and what is not? and, after all, the simplified ruleset explicitly mentiones

ignore all rules – rules on wikipedia are not fixed in stone. the spirit of the rule trumps the letter of the rule. the common purpose of building an encyclopedia trumps both.

i can pretty well understand that not every small band hobby band project should be mentioned – in particular the ones which sound bad and dissolve quickly with none or almost no productions. but that’s not the case for mar de grises. besides that, the deletion log also mentiones other problems with the article (namely, being badly written and failling to provide references for some claims), but why not throw these parts out or reduce the article to a stub?
two other examples, this time from the german wikipedia, are sinnlos im weltraum and lord of the weed, two fandubs. according to the english wikipedia, sinnlos im weltraum (a redub of a star trek series), dating back to 1994, is one of the first such projects, essentially starting the whole genre of fandubs. i don’t know how many people know it, probably a huge number. lord of the weed (a redub of the beginning of 2001’s lord of the rings) is also rather well-known; i don’t remember how often i saw it – at least ten times. well, it is obviously true that these movies haven’t been shown in movie theaters or on television – as they contain copyrighted material (i.e. the original movie), used without permission. for the same reason, they haven’t been shown on film festivals, you can’t buy them on dvd. they are also not listed on the imdb. but – so what? does that make them not noteable? irrelevant?
on the other hand, a lot of totally trashy movies – which, compared to sinnlos im weltraum and lord of the weed, are really crappy and lame – are featured on media, two good examples are a music video by grup tekkan and the infamous star wars kid, making a fool out of himself. these are pushed by media as “youtube movies you have to see” or are even shown on tv. and they can be found on wikipedia. even though they are real crap. in the case of star wars kid, the really embarrassing movie was uploaded by “friends” of its actor and will probably haunt him for a very long time. to make this even better, a lot of online versions of famous newspapers or magazines feature this video as well, showing it to an even wider audience. and i thought the use of a pillories are outlawed in modern countries.
anyway. i’m still using wikipedia, even though of these reasons. and i even created an account at the english wikipedia and started writing an article about infrastructures (number theory). as so far, nobody else dared to write something on this subject, and a google search only gives documents featuring other kinds of infrastructures, or scientific articles about this subject, i thought it would be time to add something to the web. i’ve started a series of posts on my math blog on infrastructures, but as google usually ranks wikipedia articles higher, i decided to also add something to wikipedia. so far, it is more a stub and far from being a complete article, but at least provides some information and several references to literature.

i finally started another project: a math blog. the aim of this one is to write about mathematical things which interest me, for example things related to my research. the formulae will be rendered with latex; mathml is simply unuseable so far.
an example post shows a feature with i added to my wp-latex enhancer plugin: (primitive) environments for definitions, theorems, proofs, etc., including a very basic labeling system allowing hyperlinks which jump to the right environment; for example, here’s a link to a lemma in the post. the post features my favourite proof of the fundamental theorem of algebra, using complex analysis.

i was thinking on using latex in maybe some blog entries, maybe here or maybe somewhere else. so i decided to see what existing plugins there are. after a bit of searching, i stumbled over wp-latex, which is apparently also used by wordpress.com. unfortunately, it has a kind of clumsy syntax (“$latex formula$” instead of simply “$formula$”). and it has no support for display style formulae, i.e. something centered in its own line, as opposed to inline formulae which try to fit neatly into the text.
so i tried to fix that. and it worked out, and i can still use a “normal” $ by appending a blackslash in front of it. well, euler’s identity is , as simple as that. if you want to see something more complicated:

let be a number field or an algebraic function field. then, we have the following commutative diagram with exact rows and columns:

here, simply denotes the cokernel of the map which assigns to every unit its principal divisor ; in particular, . finally, denotes the cokernel of the degree map , where in the number field case, , and in the function field case, .

this is written as follows:

let $K$ be a number field or an algebraic function field. then, we have the following commutative diagram with exact rows and columns:
$$\xymatrix{ & 0 \ar[d] & 0 \ar[d] & 0 \ar[d] & \\ 0 \ar[r] & \calO^* / k^* \ar[r] \ar[d] & \Div^0_\infty(K) \ar[r] \ar[d] & T \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / k^* \ar[r] \ar[d] & \Div^0(K) \ar[r] \ar[d] & \Pic^0(K) \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / \calO^* \ar[r] \ar[d] & \Id(\calO) \ar[r] \ar[d] & \Pic(\calO) \ar[r] \ar[d] & 0 \\ & 0 & H \ar@{=}[r] \ar[d] & H \ar[d] & \\ & & 0 & 0 & }$$
here, $T$ simply denotes the cokernel of the map $\calO^* \to \Div^0_\infty(K)$ which assigns to every unit $\varepsilon \in \calO^*$ its principal divisor $(\varepsilon)$; in particular, $T \cong \Div^0_\infty(K) / (\Princ(K) \cap \Div^0_\infty(K))$. finally, $H$ denotes the cokernel of the degree map $\Div(K) \to \G$, where in the number field case, $\G = \R$, and in the function field case, $\G = \Z$.

note that this example also shows a problem: namely, the vertical alignment of the inline formulae sucks bigtime. let’s see how to fix this…

this week, i was attending the ants. that’s not a conference on ant colony optimization and swarm intelligence, but the eighth instance of the algorithmic number theory symphosium, held in banff, canada.
banff is situated in the canadian part of the rocky mountains, whence one has a pretty neat sight:

here are some impressions from the conference center facilities. the first is a shortcut to the dining hall, the second the professional develop center, and the third one a pathway inbetween:

the next two photos show a view from inside the professional develop center, where we were housed, and me together with my poster:

this conference has been really great. i had lots of fun, learned a lot, met a lot of nice folks (again). and some more.

mathematics is nothing but the search for structures. beautiful structures. i myself tend to think i understood something if i manage to have a picture of it in my head, some geometric interpretation. sometimes it’s more easy to understand something if one can somehow draw it, by hand, or using a computer, which can sometimes give insights which would not be possible without it; the best example maybe is the beautiful mandelbrot set. most visualizations are by no means as impressive as the mandelbrot set, unless the viewer is acquainted with the underlying mathematics. like the following one, produced by the programs i wrote yesterdays and today, whose beauty probably won’t unfold if you don’t know what it depicts:

do you know the feeling when, while doing something completely unrelated, like taking a shower, you get an idea? an idea which is somehow cool, which will change life completely, in some sense? with such ideas, usually lots of endorphines and adrenaline is set free, making you unable to sleep, to rest, to think clearly. then, after spending the day working the idea out, you finally notice a tiny flaw, something that didn’t worked as smoothly as you thought it would or should. such tiny, but yet so fatal, killing the whole idea, throwing you back to the ground of the pit, where you continue to lurk around, in search for new ideas. but then, it’s not as bad as it sounds. usually you learn something. you get a better understanding of something, the object in question has turned into something which you can see better with your mind, from a bit farer away, not as near as before, so near that you can see every bump but have no clue what these bumps belong to. like a new stack of jigsaw pieces, given to you to plug it into your big world puzzle, to complete it a bit more, to widen your glance on the truth. the universe got a bit smoother.

no, this post is not about the area of abstract algebra in mathematics, but about the experimental metal project abstrakt algebra founded after candlemass‘ dismanteling by leif edling. they released one album and started with a second, but ran out of money, and leif ended up escaping bankrupcy by re-using some of the second albums material to create another candlemass album, dactylis glomerata (named after a flower he’s allergic to). the 2006 reissue of dactylis glomerata contains as a bonus disk the unfinished version of the second abstrakt algebra album, entitled abstrakt algebra ii (now guess how the first one was called). well. the arrival of that one kicked me out of bed this morning, when the mailman rang the doorbell. but it was worth getting up for it, and even if it is not a very good album, it is not good, it is interesting, and it is one of the albums every mathematician who has a similar strange taste of music than me should have in his cd shelf. of course, together with their first album, which i just ordered. ;-)

yesterday i started reading the xkcd archives (maybe you’ve already noticed that yesterday). if you don’t know xkcd, it’s a webcomic “of romance, sarcasm, math, and language”. here are the ones i found particularly interesting, funny, or whatever:

• pi equals. reminds me of the classic “help, i’m trapped in a fortune cookie factory!” joke.
• what if.
• barrel – part 3. i wouldn’t say “wow!” in that situation, though.
• fourier. poor cat.
• secrets.
• useless. standard approachs suck for love.
• su doku. even i can solve these.
• national language.
• binary heart. if you check the parity of the read ones in every column, you’ll notice most of them are even. is this a coincidence? (and don’t ask why i stumbled about that…)
• laser scope. sometimes the primitive word jokes are the best.
• riemann-zeta. about love & primes. this one is not only for number theorists.
• nihilism. squirrels! cool!
• alice and bob. the real story of eve.
• matrix transform. if i’d ever had to solve linear algebra exercises again, i’d try to turn this one in.
• valentine’s day. nothing to add.
• cat proximity. yay, how true. meow!
• code talkers. another one on cryptography.
• fixed width. nerd talk on irc. i don’t know what scares me more, laughing about this one or thinking that i’m probably knowing people who would really do this.
• exploits of a mom. well. if you don’t know what an sql injection attack is, read about it here.

consider the field of all numbers. meaning, of course, the complex numbers. we say that a number is representable if we can describe it by a text (for example, by a binary coded string of 0’s and 1’s of finite length). the set of all representable numbers is countable, as there’s a surjection of the set of binary strings (which is countable) onto it. moreover, it is a field, as if a and b are representable numbers, we have that a + b, a − b, a ⋅ b and a / b are represented by strings as “sum of (description of a) and (description of b)”. obviously, every algebraic number is representable, so our field of representable numbers contains the algebrically closed field of the algebraic numbers. but then, our field also contains euler’s number e and archimedes’ constant π, so it’s strictly larger. this opens the question: how does it’s algebraic closure looks like? not too surprisingly, it turns out to be already algebraically closed: every element in its closure can be represented by “root of polynomial with coefficients (description of coefficients)”, as all coefficients are representable. hence, our field, being countable, is strictly larger than the smallest algebraically closed subfield of the complex numbers, but still countable. and it contains lots of transcendental numbers. isn’t that cool?