Timeline for Examples of major theorems with very hard proofs that have not dramatically improved over time
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 4, 2014 at 16:01 | comment | added | Asaf | As Gil have asked me to add here, Ratner's proof of the Oppenheim conjecture relies on (the orbit closure theorem which relies on-)the measure-classification theorem for $SO(2,1)$-inv.+ergodic measures on $SL_{3}(\mathbb{R})/SL_{3}(\mathbb{Z})$, a few years ago, Manfred Einsiedler have given a simple proof of the measure classification theorem in such a case (action of a semi-simple group) here - math.ethz.ch/~einsiedl/omgsur.pdf | |
| Dec 21, 2013 at 15:49 | comment | added | Asaf | Nevertheless, the argument by Dani and Margulis is a bit more simplified, in the way that enabled Margulis and Lindenstrauss to prove an effective Oppenheim conjecture (the paper got released only in $2013$!, because of building on the famous work of Einsiedler-Margulis-Venkatesh about effective equidistribution of horospheres). | |
| Dec 21, 2013 at 15:47 | comment | added | Asaf | with Ratner's theorem, you are almost getting a 3 lines proof (Basically, $SO(2,1)$ is a maximal unipotent subgroup of $SL_{3}$). One might say that it builds on Ratner's MC theorem (where Margulis' proof was by purely topological dynamics in some sense), but still, I think that the people who are doing Homogeneous Dynamics would consider this a simplification, as Ratner's theorems are nowadays standard in that field and in number theory at general. | |
| Dec 20, 2013 at 12:34 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Dec 20, 2013 at 12:09 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Dec 20, 2013 at 11:48 | history | undeleted | Dietrich Burde | ||
| Dec 20, 2013 at 11:48 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
added 94 characters in body
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| Dec 20, 2013 at 11:35 | history | deleted | Dietrich Burde | via Vote | |
| Dec 20, 2013 at 11:03 | history | answered | Dietrich Burde | CC BY-SA 3.0 |