I just saw in Claire Mathieu’s blog “A CS professor blog” that a simple proof of the Sleator-Tarjan-Thurston’s diameter result for the graph of the associahedron was found by Lionel Pournin! Here are slides of his lecture “The diameters of associahedra” and link to the paper with the same title “The diameters of associahedra.” The original proof was based on hyperbolic volume computations and was quite difficult. (Here is an earlier post on the associahedron and an earlier mention of a connection found by Dehornoy with the Thompson group.)
Maybe I should say that (like every year but even more so) we do have funding for 1-2 postdoctoral positions in combinatorics, for 1-3 years starting in the next academic year (the time is flexible) here at the Hebrew University of Jerusalem. If you do research in combinatorics or in related areas you may enjoy our special environment (and weather, and sights), our lovely group of combinatorialists both in the mathematics and the computer science departments, and the other great reseach groups around. (We can supply recommendations from people who enjoyed it here and had a fruitful time.)
We can also support short term visits of graduate students and postdocs.
If you are interested, especially if you are (more or less) interested in the type of things I am doing – please send me an email. (Maybe write in the subject: “postdoctoral position in combinatorics”.)
Here is a lovely lecture starting with quantum computers, going through the Feldenkrais method, and ending with a mathematical puzzle.
Click on the picture for the video of the talk.
Here are Dorit’s four body-mind principles for learning:
1. Start within your comfort zone and make it even more conforting,
2. Not too easy not too hard, pick an interesting challenge within your reach,
3. Move away from your desired place and come back to it from different angles,
4. Play with it, connect it with other things you know, make it your own.
Lenore Holditch is a freelance writer. Here is what she wrote to me: “I love learning about new topics, so I am confident that I can provide valuable content for your blog on any topic you wish, else I can come up with a post most relevant to your blog theme. The content would be fully yours.” Lenore only asked for a link back to her site . She sent me also a few of her articles like this one about finding jobs after graduation and this one about video games for training.
I asked Lenore to explore the following issue and she agreed:
Is the game Angry Bird becoming gradually easier with new versions so people get the false illusion of progress and satisfaction of breaking new records?
The following paradox was raised by Rann Smorodinsky:
Rann Smorodinsky’s Privacy Paradox
Suppose that you have the following one-time scenario. You want to buy a sandwich where the options are a roast beef sandwich or an avocado sandwich. Choosing the sandwich of your preference (say, the avocado sandwich) adds one to your utility, but having your private preference known to the seller, reduces by one your utility. The prior people have on your preferences is fifty-fifty.
If you choose the avocado sandwich your utility is zero, hence you can improve on this by picking each type of sandwich at random with probability 1/2. In this case your private preference remains unknown and you gain in expectation 1/2 for having the sandwich you prefer with probability 1/2.
But given this strategy, you can still improve on it by choosing the avocado sandwich.