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SUMMARY:Integer distance sets - Sarah Peluse (University of Michigan)
DTSTART:20240412T130000Z
DTEND:20240412T140000Z
UID:TALK214045@talks.cam.ac.uk
DESCRIPTION:I'll speak about new joint work with Rachel Greenfeld and Mari
 na Iliopoulou in which we address some classical questions concerning the 
 size and structure of integer distance sets. A subset of the Euclidean pla
 ne is said to be an integer distance set if the distance between any pair 
 of points in the set is an integer. Our main result is that any integer di
 stance set in the plane has all but a very small number of points lying on
  a single line or circle. From this\, we deduce a near-optimal lower bound
  on the diameter of any non-collinear integer distance set of size n and a
  strong upper bound on the size of any integer distance set in [-N\,N]^2 w
 ith no three points on a line and no four points on a circle.
LOCATION:Seminar Room 1\, Newton Institute
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