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UID:e8055fcf31f33256f1889f8f09160af5
CATEGORIES:Colloquia
CREATED:20260127T114232
SUMMARY: Beyond translation-invariance in arithmetic harmonic analysis
LOCATION:Hill 705
DESCRIPTION:Essentially optimal estimates have been obtained for mean values of Vinogra
 dov’s exponential sum as a consequence of the decoupling method (by Bourgai
 n, Demeter and Guth), and the efficient congruencing method (by the speaker
 ). Such work makes essential use of the fact that the system of Diophantine
  equations associated with these mean values is translation-dilation invari
 ant. We sketch out such ideas, and report on progress for systems which are
  not translation-dilation invariant obtained by exploiting the arithmetic o
 f function fields over the field of p-adic numbers. Counting problems for D
 iophantine equations feature prominently.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Essentially optimal estimates have been obtained for mean values of Vino
 gradov’s exponential sum as a consequence of the decoupling method (by Bour
 gain, Demeter and Guth), and the efficient congruencing method (by the spea
 ker). Such work makes essential use of the fact that the system of Diophant
 ine equations associated with these mean values is translation-dilation inv
 ariant. We sketch out such ideas, and report on progress for systems which 
 are not translation-dilation invariant obtained by exploiting the arithmeti
 c of function fields over the field of p-adic numbers. Counting problems fo
 r Diophantine equations feature prominently.</p>
CONTACT:Trevor Wooley
DTSTAMP:20260827T051731
DTSTART;TZID=America/New_York:20260401T033000
DTEND;TZID=America/New_York:20260401T163000
SEQUENCE:0
TRANSP:OPAQUE
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