Timeline for Model-theoretic construction of Gromov boundaries on groups
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| May 23 at 9:04 | comment | added | CatsAndDogs | @NWMT This sounds very interesting, I'll talk with my supervisor and see if that's a possible project! Thanks for the suggestion ^-^ | |
| May 21 at 12:38 | comment | added | NWMT | I actually think this is a feasible problem. Non-principal ultrafilters are things that find convergent subsequences. Gromov boundaries are sets of limit points of geodesics modulo some equivalence relations. I think it could be interesting to construct Gromov boundaries using some kind of ultralimit. It may be "trivial" but definitely appropriate for an undergraduate project as it will require digesting two heavy duty definitions. All that said, amenability will play no role here. | |
| May 20 at 20:56 | comment | added | CatsAndDogs | @MoisheKohan He's just a busy guy, that's all. I'm sure he knows enough about the relevant material, he's just seen a lot of work. | |
| May 20 at 18:56 | comment | added | Dmitrii Korshunov | @AlessandroCodenotti you probably mean arxiv.org/abs/math/0311101 Linus Kramer & Katrin Tent "Asymptotic cones and ultrapowers of Lie groups" | |
| May 20 at 18:37 | history | edited | YCor | CC BY-SA 4.0 |
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| May 20 at 18:33 | comment | added | Alessandro Codenotti | If I remember correctly Katrin Tent has some papers (together with a few coauthors) on asymptotic cones that might be relevant (but I do agree with the second half of Moishe's comment) | |
| May 20 at 17:39 | comment | added | Moishe Kohan | Gromov's theorem on groups of polynomial growth and elementary logic, van den Dries, L.; Wilkie, A. J., J. Algebra 89 (1984), no. 2, 349–374. Sorry to say, but it does not sound like your professor knows enough of the relevant material to supervise student's research project on this subject... | |
| May 20 at 17:34 | comment | added | CatsAndDogs | @MoisheKohan He's trying to find it too. You mentioned the asymptotic cone, is there a paper about a model-theoretic construction of that? Maybe it's that he was talking about. | |
| May 20 at 17:31 | comment | added | Moishe Kohan | Why don't you ask your professor about details? Also, maybe your professor confused Gromov-boundary and the asymptotic cone... | |
| S May 20 at 17:25 | review | First questions | |||
| May 20 at 17:47 | |||||
| S May 20 at 17:25 | history | asked | CatsAndDogs | CC BY-SA 4.0 |