Computation speedup

[piotrmizerka]

A short report on the numbers & times of some problems we solved (note that some of numbers and times may be very tentative as I don't remember them exactly):

(1) Wedderburn for $\Delta_1$ of SAut($F_4$) supported on ball of radius 2 using wreath product action:

• size of psd constraint before Wedderburn: 85_000 x 85_000
• size of psd blocks after Wedderburn: 1344, 1287, 1348, 1283, 2264, 1193, 1071, 705, 1088, 383, 322, 1027, 218, 329, 111, 107, 325, 1290, 649, 641
• execution time: about 3 weeks

(2) Wedderburn for $\Delta_1$ of SAut($F_4$) supported on ball of radius 2 using symmetric group action:

• size of psd constraint before Wedderburn: 43_000 x 43_000
• size of psd blocks after Wedderburn: 3554, 5396, 1842, 1712, 5266
• execution time: about 1 - 2 weeks

(3) Wedderburn for "classical" Kazhdan, i.e. $\Delta^2-\lambda\Delta$, for SAut($F_4$) supported on ball of radius 3 using wreath product action:

• size of psd constraint before Wedderburn: 58_000 x 58_000
• size of psd blocks after Wedderburn (a report of the run by @kalmarek from December 2022): the biggest block of size 1500, 10 blocks bigger than 500
• execution time: I don't remember - now I am running this again - it's been running since 10 days already, not completed.

(4) Wedderburn for $\Delta_1$ of SAut($F_4$) supported by the differentials' support only using symmetric group action:

• size of psd constraint before Wedderburn: about 15_000 x 15_000
• size of psd blocks after Wedderburn: I don't remember now
• execution time: I don't remember now
• logs from the solvers (none of them certified): https://docs.google.com/document/d/1KEFxSS24aAmxuNIeSjWVBy03g29Q52X1TN_m3WVZu_0/edit?usp=sharing

(5) Some big non-Wedderburn problems concerning computation of higher degree spectral gaps for SL(4,Z): https://docs.google.com/document/d/1cyNSVou6DQK4VLM1R9ajPjnR6yGOmcsjAFfFn4VORyg/edit?usp=sharing