- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 17, 2016 - 11:05am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Andrew Suk – University of Illinois at Chicago
- Organizer
- Shahaf Nitzan

The
classic 1935 paper of Erdos and Szekeres entitled ``A combinatorial
problem in geometry" was a starting point of a very rich discipline
within combinatorics: Ramsey theory. In that paper, Erdos and Szekeres
studied the following geometric problem. For every integer n \geq 3,
determine the smallest integer ES(n) such that any set of ES(n) points
in the plane in general position contains n members in convex position,
that is, n points that form the vertex set of a convex polygon. Their main result showed
that ES(n) \leq {2n - 4\choose n-2} + 1 = 4^{n -o(n)}. In 1960, they
showed that ES(n) \geq 2^{n-2} + 1 and conjectured this to be optimal.
Despite the efforts of many researchers, no improvement in the order of
magnitude has been made on the upper bound over the last 81 years. In
this talk, we will sketch a proof showing that ES(n) =2^{n +o(n)}.