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SUMMARY:Oleksiy Klurman (University of Bristol)
DTSTART:20231214T171500Z
DTEND:20231214T183000Z
DTSTAMP:20260423T022036Z
UID:NEDNT/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/69/">F
 inding Infinite arithmetic structures in sets of positive density</a>\nby 
 Oleksiy Klurman (University of Bristol) as part of New England Dynamics an
 d Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIs there a
  partition of the natural numbers into finitely many pieces\, none of whic
 h contains a Pythagorean triple (i.e. a solution to the equation x^2 + y^2
  = z^2)? This is one of the simplest (to state!) questions in arithmetic R
 amsey theory which is still widely open. I will talk about a recent partia
 l result\, showing that “Pythagorean pairs” are partition regular\, th
 at is in any finite partition of the natural numbers there are two numbers
  x\,y in the same cell of the partition\, such that x^2 + y^2 = z^2 for so
 me integer z (which may be coloured differently). The proof is a blend of 
 ideas from ergodic theory and multiplicative number theory. Based on a joi
 nt work with N. Frantzikinakis and J. Moreira.\n
LOCATION:https://researchseminars.org/talk/NEDNT/69/
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