 CARMAGTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR
 Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle
 Title: Dependent Random Choice II
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Thu, 17^{th} Nov 2011
 Abstract:
We look at (parts of) the survey paper Dependent Random
Choice by Jacob Fox and Benny Sudakov: http://arxiv.org/abs/0909.3271. The abstract of the paper says "We describe a simple and yet
surprisingly powerful probabilistic technique which shows how to find in
a dense graph a large subset of vertices in which all (or almost all)
small subsets have many common neighbors. Recently this technique has
had several striking applications to Extremal Graph Theory, Ramsey
Theory, Additive Combinatorics, and Combinatorial Geometry. In this
survey we discuss some of them." My plan for the seminar is to start
with a quick recap of the classics of extremal (hyper)graph theory (i.e.
Turan, Ramsey, RamseyTuran), then look at some simple examples for the
probabilistic method in action, and finally come to the striking
applications mentioned in the quoted abstract. Only elementary
probability is required.
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