## Archive for April, 2010

## The McKay correspondence I

Posted in math.CO, math.GR, math.RT, tagged Dynkin diagrams, MathOverflow, walks on graphs on April 27, 2010 | 5 Comments »

## Nationals 2010

Posted in math.GR, tagged group actions on April 12, 2010 | 5 Comments »

MIT is hosting the United States Rubik’s Cube Championships this summer, August 6-8. All ages welcome! Normally I wouldn’t post about such things, but

- I happen to be a member of the Rubik’s Cube club here, and
- Some people use the Rubik’s cube group to motivate group theory. I’m a fan of hands-on mathematics, and there’s a lot to learn from the cube; for example, you quickly understand that groups are not in general commutative. The Rubik’s cube itself is also a good example of a torsor.

Actually, just so this post has some mathematical content, there’s something about the Rubik’s cube group that is probably very simple to explain, but which I don’t completely understand. It’s a common feature of Rubik’s cube algorithms that they need to switch around some parts of the cube without disturbing others; in other words, the corresponding permutation needs to have a lot of fixed points. This seems to be done by writing down a lot of commutators, but I’m not familiar with any statements in group theory of the form “commutators tend to have fixed points.” Can anyone explain this?