Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, October 13, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Joel Spencer (New York University)

The Long Journey of R(3,k)

Ramsey Theory is a fascinating topic. Here we speak of a specific problem, the Ramsey function R(3,k). The story begins with George Szekeres, Esther Klein and a young Paul Erdos walking the beautiful hills of Budapest. Results were given in 1932-3, 1946, 1968, 1980, 1995 until the asymptotic resolution (also 1995) by Jeong Han Kim that R(3,k) is within a constant of k^2/(\ln k). The story, however, didn't end. In 2009 Tom Bohman gave a new proof, analyzing the random triangle-free process. Deeper analysis, by several researchers, has recently lowered the gap between the implied constants to four. We shall outline many of the arguments which, in their own way, provide a history of the development of Ramsey Theory and the Probabilistic Method.

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