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DTSTART;TZID=America/Toronto:20260224T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-163
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:CHI HOI YIP\, GEORGIA INSTITUTE OF TECHNOLOGY\n\n_Inverse sieve
  problems_\n\nMany problems in number theory boil down to bounding the siz
 e of a set\ncontained in a certain set of residue classes mod p for variou
 s sets\nof primes p\; and then sieve methods are the primary tools for doi
 ng\nso. Motivated by the inverse Goldbach problem\, Green–Harper\,\nHelf
 gott–Venkatesh\, Shao\, and Walsh have explored the inverse sieve\nprobl
 em: if we let S \\subseteq N be a maximal set of integers in this\ninterva
 l where the residue classes mod p occupied by S have some\nparticular patt
 ern for many primesp\, what can one say about the\nstructure of the set S 
 beyond just its size? In this talk\, I will give\na gentle introduction to
  inverse sieve problems\, and present some\nprogress we made when S mod p 
 has rich additive structure for many\nprimes p. In particular\, in this se
 tting\, we provide several\nimprovements on the larger sieve bound for |S|
 \, parallel to the work\nof Green--Harper and Shao for improvements on the
  large sieve. Joint\nwork with Ernie Croot and Junzhe Mao.\n\nJoin on Zoom
 \n[https://uwaterloo.zoom.us/j/98942212227?pwd=huSbGSNTP1ODaePFVsXb4FJy6De
 ite.1%20%20Meeting%20ID:%20989%204221%202227%20Passcode:%20112827]
DTSTAMP:20260407T211618Z
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