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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Integer distance sets - Sarah Peluse (University o
f Michigan)
DTSTART;TZID=Europe/London:20240412T140000
DTEND;TZID=Europe/London:20240412T150000
UID:TALK214045AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/214045
DESCRIPTION:I'll speak about new joint work with Rachel Greenf
eld and Marina Iliopoulou in which we address some
classical questions concerning the size and struc
ture of integer distance sets. A subset of the Euc
lidean plane 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 in
teger distance 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 intege
r distance set of size n and a strong upper bound
on the size of any integer distance set in [-N\,N]
^2 with no three points on a line and no four poin
ts on a circle.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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