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LSpice
LSpice
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optimal Optimal sphere packings in dimensions different fom 8 and 24

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edit approved Sep 11, 2022 at 16:35
J. W. Tanner
edit approved Sep 11, 2022 at 16:35
J. W. Tanner
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After the broundbreaking worksgroundbreaking work of Viazovska, now we have a proof for the optimal density of sphere packings in dimensions 8 and 24. Both packings emerge from very particular algebraic lattice structures on the 8th and 24th dimensional space.

My question is somehowsomewhat philosophical: for for the rest of dimensions (except 2 and 3) there do not existsexist such structures. Is there however any extra obstruction (geometrical, algebraic) whichwhich gives evidencesevidence that no such 'rigid' algebraic structure may exist?

After the broundbreaking works of Viazovska now we have a proof for the optimal density of sphere packings in dimensions 8 and 24. Both packings emerge from very particular algebraic lattice structures on the 8th and 24th dimensional space.

My question is somehow philosophical: for the rest of dimensions (except 2 and 3) there do not exists such structures. Is there however any extra obstruction (geometrical, algebraic) which gives evidences that no such 'rigid' algebraic structure may exist?

After the groundbreaking work of Viazovska, now we have a proof for the optimal density of sphere packings in dimensions 8 and 24. Both packings emerge from very particular algebraic lattice structures on the 8th and 24th dimensional space.

My question is somewhat philosophical: for the rest of dimensions (except 2 and 3) there do not exist such structures. Is there however any extra obstruction (geometrical, algebraic) which gives evidence that no such 'rigid' algebraic structure may exist?

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Johnny Cage
Johnny Cage
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optimal sphere packings in dimensions different fom 8 and 24

After the broundbreaking works of Viazovska now we have a proof for the optimal density of sphere packings in dimensions 8 and 24. Both packings emerge from very particular algebraic lattice structures on the 8th and 24th dimensional space.

My question is somehow philosophical: for the rest of dimensions (except 2 and 3) there do not exists such structures. Is there however any extra obstruction (geometrical, algebraic) which gives evidences that no such 'rigid' algebraic structure may exist?