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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240326T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-119
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:MICAH MILINOVICH\, UNIVERSITY OF MISSISSIPPI\n\n\"FOURIER OPTIM
 IZATION\, PRIME GAPS\, AND THE LEAST QUADRATIC\nNON-RESIDUE\"\n\nThere are
  many situations where one imposes certain conditions on a\nfunction and i
 ts Fourier transform and then wants to optimize a\ncertain quantity. I 
 will describe two such Fourier optimization\nframeworks that can be used t
 o study classical problems in number\ntheory: bounding the maximum gap b
 etween consecutive primes assuming\nthe Riemann hypothesis and bounding f
 or the size of the least\nquadratic non-residue modulo a prime assuming th
 e generalized Riemann\nhypothesis (GRH) for Dirichlet L-functions. The res
 ulting extremal\nproblems can be stated in accessible terms\, but finding 
 the exact\nanswer appears to be rather subtle. Instead\, we experimentally
  find\nupper and lower bounds for our desired quantity that are numericall
 y\nclose. If time allows\, I will discuss how a similar Fourier\noptimizat
 ion framework can be used to bound the size of the least\nprime in an arit
 hmetic progression on GRH. This is based upon joint\nworks with E. Carneir
 o (ICTP)\, E. Quesada-Herrera (TU Graz)\, A. Ramos\n(SISSA)\, and K. Sound
 ararajan (Stanford). \n\nMC 5417
DTSTAMP:20260505T133058Z
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