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SUMMARY:On the size of subsets of F_p^n without p distinct elements summin
 g to zero - Lisa Sauermann (Stanford University)
DTSTART:20200219T134500Z
DTEND:20200219T144500Z
UID:TALK138439@talks.cam.ac.uk
CONTACT:Thomas Bloom
DESCRIPTION:Let us fix a prime p. The Erdös-Ginzburg-Ziv problem asks for
  the minimum integer s such that any collection of s points in the lattice
  Z&Hat\;n contains p points whose centroid is also a lattice point in Z&Ha
 t\;n. For large n\, this is essentially equivalent to asking for the maxim
 um size of a subset of F_p^n without p distinct elements summing to zero.\
 n\nIn this talk\, we discuss a new upper bound for this problem for any fi
 xed prime p\\geq 5 and large n. Our proof uses the so-called multi-colored
  sum-free theorem which is a consequence of the Croot-Lev-Pach polynomial 
 method\, as well as some new combinatorial ideas.
LOCATION:MR4\, CMS
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