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SUMMARY:Aled Walker (Cambridge)
DTSTART:20210315T160000Z
DTEND:20210315T170000Z
DTSTAMP:20260423T024026Z
UID:IML_NT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/12/">
 Poissonian gap distributions of dilated sequences</a>\nby Aled Walker (Cam
 bridge) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\
 nIn the late 1990s\, Rudnick and Sarnak conjectured that the gap\ndistribu
 tion of the sequence of dilated squares modulo 1\, at least for a\ngeneric
  dilate\, should agree with the gap distribution of a set of\nuniformly di
 stributed random points modulo 1.  This conjecture is still\ncompletely op
 en. Nonetheless\, the conjecture has stimulated a great deal\nof work\, st
 udying these gap distributions of dilated squares and dilates\nof other se
 quences\, particularly focussed on the associated correlation\nfunctions. 
 Recently\, connections were discovered to certain notions from\nadditive c
 ombinatorics and sum-product theory. In this talk I will\ndiscuss some of 
 the work I've been involved with on pair correlations\nand triple correlat
 ions related to these problems\, studying dilates of\nthe primes\, the squ
 ares\, and of generic sequences -- sometimes jointly\nwith various subsets
  of Thomas Bloom\, Sam Chow\, Ayla Gafni\, and Niclas\nTechnau.\n
LOCATION:https://researchseminars.org/talk/IML_NT/12/
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