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SUMMARY:Two Erdős problems on lacunary sequences: chromatic number and Di
 ophantine approximation - Yuval Peres (Microsoft Research)
DTSTART:20111103T143000Z
DTEND:20111103T153000Z
UID:TALK34179@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Abstract: Let {n_k} be a lacunary sequence\, i.e.\, the ratio 
 of successive elements of the sequence is at least some q>1. In 1987\, Erd
 ős asked for the chromatic number of a graph G on the integers\, where tw
 o integers are\nconnected by an edge iff their difference is in the sequen
 ce {n_k}. Y.Katznelson found a connection via a to a Diophantine approxima
 tion problem: finding irrationals x such that n_k times x is at least r>0 
 away\nfrom the integers for all k. In joint work with W.Schlag\, we improv
 e Katznelson's bounds for both problems using the Lovasz local lemma. It i
 s still an unsolved problem to obtain matching upper and lower bounds.\n
LOCATION:MR12
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