most recent 30 from http://mathoverflow.net 2013-05-22T12:30:33Z http://mathoverflow.net/feeds/question/20147 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20147/what-would-a-graduate-course-on-systolic-geometry-typically-cover Thomas Sauvaget 2010-04-02T08:11:19Z 2010-04-10T00:57:27Z

<p>It's all in the title basically. There's an interesting topic called <a href="http://en.wikipedia.org/wiki/Systolic_geometry" rel="nofollow">systolic geometry</a> that has grown a lot in the past 30 years, with a (first?) <a href="http://www.ams.org/bookstore-getitem/item=surv-137" rel="nofollow">textbook</a> on the subject by M.Katz (AMS 2007).</p> <p>So I was wondering what would a semester-long graduate course typically cover, assuming knowledge of basic Riemannian geometry. </p> <p>I haven't been able to find much information online: Katz has a <a href="http://u.math.biu.ac.il/~katzmik/egreg826.pdf" rel="nofollow">second semester graduate course</a> which doesn't quite cover the same ground as the book. Has there been other courses on the topic elsewhere?</p>

http://mathoverflow.net/questions/20147/what-would-a-graduate-course-on-systolic-geometry-typically-cover/20878#20878 Dominic Dotterrer 2010-04-10T00:57:27Z 2010-04-10T00:57:27Z

<p>This is interesting. I imagine that any course would vary quite a bit depending on who taught it.</p> <p>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.</p> <p>I have no idea. You should come up with a curriculum and post it here.</p>