Factors in random graphs and hypergraphs

Jeff Kahn

ABSTRACT: Shamir's Problem (circa 1979) asks, roughly: for a
fixed k and large m, about how many random k-subsets of
{1,2,...,km} should one choose to make it likely that the
resulting collection contains a perfect matching (that is, m
disjoint k-sets)? I'll give some context for this question and
try to say something about its resolution (due to Anders
Johansson, Van Vu and myself). 	

BIO: Jeff Kahn is a professor of mathematics at Rutgers
University notable for his work in combinatorics. Jeff received
his Ph.D from the Ohio State University in 1979. In 1993,
together with Gil Kalai, he disproved Borsuk's conjecture . In
1996 he was awarded the Pólya Prize (SIAM). In 2004, with David
Galvin he made seminal contributions to the combinatorial
theory of phase transitions. See
http://ftp.informatik.rwth-aachen.de/dblp/db/indices/a-tree/k/Kahn:Jeff.html
for some of his work.