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UID:node-3090241@mathematics.huji.ac.il
DTSTAMP:20220523T113000Z
DTSTART:20220523T113000Z
DTEND:20220523T130000Z
SUMMARY:HUJI NT Seminar - Lior Bary-Soroker
DESCRIPTION:*Title*: ProbabilisticGalois Theory, the square discriminant case.\n*Abstract*: Consider the easiest model of random polynomials with integers \ncoefficients,\nwhere we fix the degree n=deg f and we choose the coefficients uniformly at \nrandom from a large box and let its size L go to infinity.\nProbabilisticGalois theory, in its naviest form, asks for the distributionof \nthe Galois group of f.\nIn 1936, Van der Waerden proved that the Galois group of the polynomial is \nthe full symmetric group S_n asymptotically almost surely.\nHe conjectured that thesecond most probable group is S_{n-1}. This conjecture \nhas seen a lot of progress along the years.\nRecently, there was a big breakthroughby Bhargava who showed that thesecond \nmost probable group is eitherS_{n-1} or A_n.\nThe breakthrough main achievement was the new upper bound C/L on the \nprobability of the Galois group being A_n.\nOne may believe that, in fact, the probability for A_n must be much smaller; \nthe goal of the talk is to discuss what should be\nthe pr...
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