Timeline for How to recognise that the polynomial method might work
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| May 18, 2016 at 2:44 | comment | added | Terry Tao | I think I'll leave the 2010 version as a record of what people like myself thought at the time. (For context: in May 2016, there was a breakthrough on the capset problem at quomodocumque.wordpress.com/2016/05/13/bounds-for-cap-sets .) | |
| May 18, 2016 at 1:44 | comment | added | Anurag | Time for an edit regarding the capset problem :) | |
| Mar 15, 2011 at 16:31 | comment | added | ACL | I don't know if my comment has a chance of being detected. Anyway: people in Diophantine geometry have been using the polynomial method and studying the Zariski complexity of sets for a long time. Pascal's theorem (about points on conics), its generalization by Cayley-Bacharach are also typical examples of that. The Schneider-Lang theorem of Bombieri bounds the Zariski complexity of the set of points at which some meromorphic function of finite order (in $n$ variables) together with its derivatives takes its values in a given number field. Amoroso-David's extension of Lehmer conjecture. | |
| Oct 26, 2010 at 7:07 | comment | added | Seva | I wonder whether this has anything to do with the notion of complexity of sets in elementary abelian $2$-groups I thought on some five+ years ago. Specifically, I defined the complexity of a set $S\subset{\mathbb F}_2^n$ as the length of the shortest chain $\emptyset=S_0\subset\dotsb\subset S_k=S$ such that for each $i\in[k]$ we have either $S_i=S_{i-1}\cup H$, or $S_i=S_{i-1}\setminus H$, for a subgroup $H\le{\mathbb F}_2^n$. I have never had any applications to this notion though, neither could I prove anything really ingenious about it. | |
| Oct 25, 2010 at 17:34 | history | edited | Terry Tao | CC BY-SA 2.5 |
added 399 characters in body; added 3 characters in body
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| Oct 25, 2010 at 17:29 | history | answered | Terry Tao | CC BY-SA 2.5 |