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Graduate Seminar
Deepak Bal Carnegie Melllon University Title: Probabilistic combinatorics and Ramsey theory. Abstract: In the 1950's Paul Erdos pioneered the use of the probabilistic method. Basically, rather than constructing combinatorial objects explicitly, one can consider an appropriate probability space and show that in that space, the probability of the desired object is nonzero. This method has proven to be indispensable in the field of combinatorics. In this talk I will show a lower bound on the Ramsey number R(k,k) and will also prove the existence of graphs with abitrarily high girth and chromatic number. If there is enough time, I will present a proof of the Weierstrass approximation theorem (while this isn't really an application of the probabilistic method, it is a nice application of probabilistic ideas to another field). Date: Tuesday, October 26, 2010 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Daniel Spector 