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DESCRIPTION: We study the Lonely Runner Conjecture\, conceived by Wills in
the 1960's: Given positive integers n_1\, n_2\, ...\, n_k\, there exists a
positive real number t such that for all 1 ≤ j ≤ k the distance of tn_j to
the nearest integer is at least 1/(k+1). Continuing a view-obstruction appr
oach by Cusick and recent work by Henze and Malikiosis\, our goal is to pro
mote a polyhedral ansatz to the Lonely Runner Conjecture. Our results inclu
de geometric proofs of some folklore results that are only implicit in the
existing literature\, a new family of affirmative instances defined by the
parities of the speeds\, and geometrically motivated conjectures whose reso
lution would shed further light on the Lonely Runner Conjecture.
DTSTAMP:20190417T162000
DTSTART:20190617T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Matthias Beck (San Francisco State University): Lonely Runner Polyh
edra
UID:95691132@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190617-L-Beck.html
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