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Sphere packings : what next after the recent breakthrough of ViasovskaViazovska (et al.)?

Given the march 2016 breakthrough concerning sphere packings by ViasovskaViazovska for the case of dimension 8, and by Cohn, Kumar, Miller, Radchenko and ViasovskaViazovska for the case of dimension 24, it follows that the known cases $\Delta_1=1$, $\Delta_2=\frac{\pi}{\sqrt{12}}$, $\Delta_3=\frac{\pi}{\sqrt{18}}$, $\Delta_8=\frac{\pi^4}{384}$ and $\Delta_{24}=\frac{\pi^{12}}{12!}$ all have a lattice solution with neat number-theoretic properties, yet the densities obtained do not seem to follow any obvious pattern, except for the presence of $\pi$.

Question A: Is there a consensus among experts that one should not hope for a synthetic formula for densities, or are there still reasonable candidate formulas standing ?

and

Question B: are there workshops planned on the recent papers soon (say, this fall, maybe even this summer) ?

Sphere packings : what next after the recent breakthrough of Viasovska (et al.)?

Given the march 2016 breakthrough concerning sphere packings by Viasovska for the case of dimension 8, and by Cohn, Kumar, Miller, Radchenko and Viasovska for the case of dimension 24, it follows that the known cases $\Delta_1=1$, $\Delta_2=\frac{\pi}{\sqrt{12}}$, $\Delta_3=\frac{\pi}{\sqrt{18}}$, $\Delta_8=\frac{\pi^4}{384}$ and $\Delta_{24}=\frac{\pi^{12}}{12!}$ all have a lattice solution with neat number-theoretic properties, yet the densities obtained do not seem to follow any obvious pattern, except for the presence of $\pi$.

Question A: Is there a consensus among experts that one should not hope for a synthetic formula for densities, or are there still reasonable candidate formulas standing ?

and

Question B: are there workshops planned on the recent papers soon (say, this fall, maybe even this summer) ?

Sphere packings : what next after the recent breakthrough of Viazovska (et al.)?

Given the march 2016 breakthrough concerning sphere packings by Viazovska for the case of dimension 8, and by Cohn, Kumar, Miller, Radchenko and Viazovska for the case of dimension 24, it follows that the known cases $\Delta_1=1$, $\Delta_2=\frac{\pi}{\sqrt{12}}$, $\Delta_3=\frac{\pi}{\sqrt{18}}$, $\Delta_8=\frac{\pi^4}{384}$ and $\Delta_{24}=\frac{\pi^{12}}{12!}$ all have a lattice solution with neat number-theoretic properties, yet the densities obtained do not seem to follow any obvious pattern, except for the presence of $\pi$.

Question A: Is there a consensus among experts that one should not hope for a synthetic formula for densities, or are there still reasonable candidate formulas standing ?

and

Question B: are there workshops planned on the recent papers soon (say, this fall, maybe even this summer) ?

Source Link
Archie
  • 883
  • 1
  • 12
  • 18

Sphere packings : what next after the recent breakthrough of Viasovska (et al.)?

Given the march 2016 breakthrough concerning sphere packings by Viasovska for the case of dimension 8, and by Cohn, Kumar, Miller, Radchenko and Viasovska for the case of dimension 24, it follows that the known cases $\Delta_1=1$, $\Delta_2=\frac{\pi}{\sqrt{12}}$, $\Delta_3=\frac{\pi}{\sqrt{18}}$, $\Delta_8=\frac{\pi^4}{384}$ and $\Delta_{24}=\frac{\pi^{12}}{12!}$ all have a lattice solution with neat number-theoretic properties, yet the densities obtained do not seem to follow any obvious pattern, except for the presence of $\pi$.

Question A: Is there a consensus among experts that one should not hope for a synthetic formula for densities, or are there still reasonable candidate formulas standing ?

and

Question B: are there workshops planned on the recent papers soon (say, this fall, maybe even this summer) ?