# ICTP Summer School and Conference on Hodge Theory

Thursday, July 01st, 2010 | Author:

Writing from my very last day at the ICTP in Miramare (Trieste), Italy, I thought it's time to summarise some impressions, as promised. First, some remarks on the ICTP and sightseeing around Miramare (which might be useful to future visitors), then I will comment on the Summer School and finally the Conference on Hodge Theory and Related Topics.

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# Mass renaming papers with BibTex+JabRef export filters

Monday, June 28th, 2010 | Author:

If you manage your (scientific) references, such as journal articles, arXiv papers and textbooks within some reference management system that uses BibTex as storage/export format, and you have local copies of your files, then the following might be of interest:

I wrote a JabRef export filter that takes a BibTex file with file links (so, BibTex fields of the form file={somefile.pdf}) and writes a linux shell script to rename the files systematically according to the scheme [bibtexkey] - [authors] - [title].[extension]. Then JabRef can find the file again via its automatic file association mechanism. I use lower-case bibtexkeys but the export filter is easily adaptable, read about it on the JabRef custom export filter documentation page.

Just create (or download) a file named "renamer.layout" and fill in this line:
\begin{file}mv "\format[FileLink]{\file}" "\format[ToLowerCase,FormatChars]{\bibtexkey} - \format[AuthorNatBib,ToLowerCase,FormatChars,RemoveBrackets]{\author} - \format[FormatChars,RemoveBrackets,ToLowerCase]{\title}.\format[Replace(.*:,),ToLowerCase]{\file}"\end{file}
then open JabRef and go to the menu entry Options->Manage custom exports->Add new where you enter (for example) "renamer" as Export name, the full path to your renamer.layout file in the Main layout file field and "sh" as File extension.

Then open your BibTex file (.bib) with JabRef and then select the menu entry File->Export and select in the drop-down-menu Files of Type your newly created export filter renamer (*.sh). This gives you a shell script which, if executed, renames all files linked from the BibTex document into a standardised format (and moves all into the directory from where you execute the script).

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# Talk notes on Bott periodicity (in german)

Monday, June 14th, 2010 | Author:

Since I wrote this, I thought someone might find it useful, so I share it with you:

Notes from a talk I gave in a student's seminar in Freiburg:
Komplexe K-Theorie: Bott-Periodizitaet (complex K-Theory: Bott periodicity)

It's almost the same proof as in Aityah's nice book, but maybe a little bit more lengthy (and in german).

... right now I'm sitting in the library at the ICTP in Miramare/Trieste, Italy. It's a beautiful place, and I think I'll write something about the summer school on Hodge Theory here, soon!

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# Why believing in conspiracy theories is wrong

Friday, May 07th, 2010 | Author:

I guess most people who believe in conspiracy theories either have some benefit in pretending to believe or they really think the theories are likely to be true. Those who think conspiracy theories are likely to be true, are victims of some kind of "Bayesian fallacy":

Bayes (English mathematician, 1702-1761) proved a theorem about conditional probabilities, nowadays called "Bayes' theorem". Suppose there are two statements A and B, which might overlap (e.g. A="it's raining today" and B="it's raining the whole week"¹, where the truth of B implies the truth of A). Now imagine these statements are more or less likely, so you attach some probability to these statements, p(A) and p(B), with values in 0-100% (or, for the mathematically oriented readers: let p be a probability measure on some discrete $\sigma$-algebra containing A and B). It's not only the probability of A and B we might be interested in, but also the conditional probability "How likely is A when B is true?", which we write p(A|B). Bayes' theorem now reads:
$P(A|B)\cdot P(B) = P(B | A)\cdot P(A)$, and this means in words, that the probability of A under the condition that B is true, multiplied by the probability of B, is the same as the probability of B under the condition that A is true, multiplied by the probability of A.

Category: English, Not Mathematics | Comments off

# A manifold whose functions are the smooth functions on the real line with rational period

Wednesday, March 31st, 2010 | Author:

Jet Nestruev: Smooth Manifolds and Observables, Springer, 2003

about a month ago (after I stumbled over a question on MO) and there was an exercise that resisted solution for more than a week.

Well.... now I found out that I have just misread the exercise. However, this way I basically did several exercises at once. Here comes the problem and its solution:

## The problem

(inspired by page 28, chapter 3, exercise 3.17.5 in Nestruev)

Find a smooth (real) manifold $M$ such that its algebra of smooth functions $C^\infty(M,\mathbb R)$ is isomorphic to the algebra of all smooth functions $f : \mathbb R \to \mathbb R$ that have some rational period $\tau$ (i.e. there exists $\tau \in \mathbb Q$ such that $f(x)=f(x+\tau)$ for all x). Note that we don't fix a period $\tau$ here. Let's call the algebra in question (smooth functions on the real line with some rational period) $A$.

You might want to stop reading here and think for a second (or minutes) about the solution or similar problems that have easier solutions. A more vague problem would be

Find a space $M$ such that the functions $M \to \mathbb R$ correspond to functions $\mathbb R \to \mathbb R$ that are periodic with some rational period.

Category: English, Mathematics | One Comment

# A survey of GNU/Linux shortcomings

Sunday, February 14th, 2010 | Author:

A long time ago, I switched from Micro\$oft Windows to GNU/Linux. Since Ubuntu, I even recommend GNU/Linux to non-computerfreaks. Sadly, Ubuntu is not perfect. In particular, some applications are still missing. What follows is a wish-list of future Ubuntu features/applications. Some of these are available on Windows or Mac OSX, most aren't.
Continue reading «A survey of GNU/Linux shortcomings»

Category: English | One Comment