Timeline for Extremal lattices
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2021 at 5:07 | comment | added | David Roberts♦ | @HenryCohn the updated links for the papers in your comment are Enumerating perfect forms and A Mordell Inequality for Lattices over Maximal Orders, respectively | |
| Oct 5, 2021 at 5:05 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
fixed arxiv front-end links and gave doi links
|
| Mar 17, 2011 at 3:44 | comment | added | Henry Cohn | I imagine that before n gets too large, the problem will become utterly intractable. However, this could be overly pessimistic. Incidentally, there are also lots of interesting questions for other rings (say, lattices with Gaussian, Eisenstein, or Hurwitz structures). See, for example, front.math.ucdavis.edu/0901.1587 and front.math.ucdavis.edu/0810.2336. | |
| Mar 17, 2011 at 3:39 | comment | added | Henry Cohn | Getting bounds (upper or lower) on the optimal lattice packing density is definitely an active topic of research. Finding exact answers is trickier, since there aren't many good opportunities. I don't know whether anyone is actively working on n=9, but maybe it will be solved in the next decade. I don't think there's much likelihood of reaching another non-consecutive value of n (like n=24), but of course it is difficult to predict. I hope n=10 will be doable someday, since that seems to be the first case in which lattices are inferior to nonlattice packings. | |
| Mar 16, 2011 at 22:00 | comment | added | Portland | Thanks Henry, very useful. Is it still an active topic of research? Do you believe there is "reasonable hope" to crack the problem for other values of $n>9$? | |
| Mar 16, 2011 at 4:23 | history | answered | Henry Cohn | CC BY-SA 2.5 |