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SUMMARY:Nikita Shulga (University of Sydney)
DTSTART:20261020T120000Z
DTEND:20261020T130000Z
DTSTAMP:20261026T125257Z
UID:OWNS/172
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/172/">N
 ine-distance theorem in three-dimensional space</a>\nby Nikita Shulga (Uni
 versity of Sydney) as part of One World Numeration seminar\n\n\nAbstract\n
 The classical three-distance theorem (also known as the Steinhaus conjectu
 re) states that the gaps determined by a finite one-dimensional Kronecker 
 sequence have at most three distinct lengths. We prove that its natural $d
 $-dimensional analogue has at most $2^d+1$ distinct lengths\,  which is th
 e optimal bound in dimensions $d=1\,2\,3$. This proves the conjecture of H
 aynes and Marklof about 3-dimensional distances.\n
LOCATION:https://researchseminars.org/talk/OWNS/172/
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