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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20250514T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-79
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ZHENCHAO GE\, UNIVERSITY OF WATERLOO\n\nAn additive property fo
 r product sets in finite fields.\n\nLagrange's Four Square Theorem states 
 that every natural number can be\nwritten as a sum of four squares\, i.e. 
 squares form an additive basis\nof order 4. Cauchy observed that in a fini
 te field F with q elements\,\nsquares form an additive basis of order 2. B
 ourgain further\ngeneralized the problem and proved that for any subset A 
 in F\, writing\nAA={aa': a\,a'∈ A}\, we have 3AA=F whenever |A|>q^{3/4}.
  \n\nIn general\, for subsets A\,B in F with |A||B|>q\, one might ask tha
 t how\nmany copies of AB are enough to cover the entire space? The current
 \nrecord of this problem is due to Glibichuk and Rudnev. Using basic\nFour
 ier analysis tools\, they achieved 10AB=F unconditionally and 8AB=F\nassum
 ing symmetry (or anti-symmetry).\n\nIn this talk\, we will (hopefully) go 
 through the paper of Glibichuk\nand Rudnev.\n\nMC 5417
DTSTAMP:20260504T180047Z
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