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SUMMARY:Bhuwanesh Rao Patil (PDF at IISER Berhampur\, India)
DTSTART:20200603T143000Z
DTEND:20200603T145500Z
DTSTAMP:20260423T011159Z
UID:CANT2020/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/32/
 ">Geometric progressions in syndetic sets</a>\nby Bhuwanesh Rao Patil (PDF
  at IISER Berhampur\, India) as part of Combinatorial and additive number 
 theory (CANT 2021)\n\n\nAbstract\nIn this talk\, we will discuss the prese
 nce of arbitrarily long geometric progressions \nin syndetic sets\, where 
 a subset of $\\mathbb{N}$ (the set of all natural numbers) \nis called \\e
 mph{syndetic} if it intersects every set of $l$ consecutive natural number
 s \nfor some natural number $l$. In order to understand it\, we will expla
 in the structure \nof the set $\\{\\frac{a}{b}\\in \\mathbb{N}: a\, b\\in 
 A\\}$ for a given syndetic set $A$.\n\nTitle: A question of Bukh on sums o
 f dilates \\\\ \nAbstract: There exists a $p<3$ with the property that for
  all real numbers $K$ and every finite subset $A$ \nof a commutative group
  that satisfies $|A+A| \\leq K |A|$\, the dilate sum \\[A+2 \\cdot A = \\{
  a + b+b : a\, b \\in A\\}\\] \nhas size at most $K^p |A|$. This answers a
  question of Bukh. \n\nJoint work with Brandon Hanson.\n
LOCATION:https://researchseminars.org/talk/CANT2020/32/
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