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It's all in the title basically. There's an interesting topic called systolic geometry that has grown a lot in the past 30 years, with a (first?) textbook on the subject by M.Katz (AMS 2007).

So I was wondering what would a semester-long graduate course typically cover, assuming knowledge of basic Riemannian geometry.

I haven't been able to find much information online: Katz has a second semester graduate course which doesn't quite cover the same ground as the book. Has there been other courses on the topic elsewhere?

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I'm a bit perplexed by the question (and not because I know nothing about systolic geometry). You ask what a graduate course on it would typically cover; but "typically" suggests that graduate courses on systolic geometry are reasonably common, or at least plural, which seems to be in doubt. Also, how long are your semesters? How many hours a week would you meet for? (Etc.) –  Tom Leinster Apr 2 '10 at 18:52
    
Exactly, that was in doubt hence the question at the end. Since there's been no quick answer, that provides a good clue that it hasn't been taught, nor is planned to be, in the US or Europe yet. A second semester in my mind goes from mid-january to end of may, with 3 hours of lectures and 2 hours of office hours per week. –  Thomas Sauvaget Apr 5 '10 at 7:39
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This is interesting. I imagine that any course would vary quite a bit depending on who taught it.

Any course should probably contain Gromov's proof of the systolic inequality for essential manifolds. Other than that, I am not sure. The course could dive into systoles on surfaces and some of the arithmetic constructions in Teichmuller theory, or it could develop harmonic maps and scalar curvature rigidity theorems, or it could take a dynamical systems approach and discuss the relationship between volume entropy and closed geodesics.

I have no idea. You should come up with a curriculum and post it here.

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Thanks for mentioning these aspects, I'll look into that (I'm a beginner on the topic, and certainly not competent to post a curriculum just yet, probably the closed geodesics aspect would be my favorite though). –  Thomas Sauvaget Apr 12 '10 at 17:54
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