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SUMMARY:Halfway to Rota's basis conjecture - Alexey Pokrovskiy (Birkbeck\,
  University of London)
DTSTART:20191205T143000Z
DTEND:20191205T153000Z
UID:TALK126526@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:In 1989\, Rota made the following conjecture. Given n bases B1
 \, ...\, Bn in an n-dimensional vector space V\, one can always find n dis
 joint bases of V\, each containing exactly one element from each Bi (we ca
 ll such bases transversal bases). Rota’s basis conjecture remains open d
 espite its apparent simplicity and the efforts of many\nresearchers (for e
 xample\, the conjecture was recently the subject of the collaborative “P
 olymath” project). In this talk\, I will discuss how to find  (0.5 - o(1
 ))n disjoint transversal bases\, improving the previously best known bound
  of n/log n.\nThis is joint work with Bucic\, Kwan\, and Sudakov.\n
LOCATION:MR12
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