Timeline for Sphere packings : what next after the recent breakthrough of Viazovska (et al.)?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 12, 2016 at 20:08 | comment | added | Yufei Zhao | I don't have a good answer I'm afraid. Our intuition for how packings work in high dimensions is rather poor. As far as I know, there is no proof that $\Delta_{n+1} \le \Delta_n$ for all sufficiently large $n$. Even if you know a good packing in $n$ dimensions, you might not get a good packing by tiling it in one higher dimension (although this strategy works well in low dimensions). See Conway and Sloane for a lot more. | |
| Apr 12, 2016 at 14:43 | comment | added | user88381 | Thanks for this answer. I was wondering, is there an intuitive answer for why the densest packing density decreases with dimension? | |
| Apr 5, 2016 at 21:07 | vote | accept | Archie | ||
| Apr 5, 2016 at 19:54 | history | edited | Yufei Zhao | CC BY-SA 3.0 |
updated link to slides
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| Apr 5, 2016 at 18:03 | history | answered | Yufei Zhao | CC BY-SA 3.0 |