我已经不知道怎么贴视频链接了，below is from blog of John Baez

"Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory---click on the picture to watch his talk. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would enjoy more.

What's great is that he's not faking it: he's really found deep ways in which symmetry shows up in music.

At first he tried to describe them geometrically using 'orbifolds', which are spaces in which some singular points have nontrivial symmetry groups, like the tip of a cone. But then he realized that the geometry was less important than the symmetry, which you can describe using groupoids: categories where every morphism is invertible. That's why his talk is called "Beyond the geometry of music".

I'm helping him with his work on groupoids, and I hope he explains his work to mathematicians someday without pulling his punches. I didn't get to interview him yesterday, but I'll try to do that soon."
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修改:vinbo FROM 202.120.11.*
FROM 202.120.11.*