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Graduate Student Combinatorics Seminar Sponsored by DIMACS

The Erdos-Szekeres conjecture

Tae Young Lee

Location:  Zoom: please email quentin.dubroff@rutgers.edu to be added to the mailing list
Date & time: Wednesday, 30 September 2020 at 12:15PM - 1:15PM

Abstract: Imagine five points in \(R^2\), where no three of them are colinear. You can always find a convex quadrilateral among them. How many points do you need for a convex pentagon? What about a convex \(k\)-gon? Is it even possible? Erdos and Szekeres proved that this is indeed possible whenever you have at least \(ES(k)\) points in general position, where \(ES(k)\) is some number not exceeding \(((2k-4)\) choose \((k-2))+1\). They conjectured that \(ES(k)=2^{k-2}+1\), and later proved that this is a lower bound. I will present their proofs about these facts and a sketch of the proof of the best known upper bound by Andrew Suk. If time permits, I will also briefly discuss some variants and generalizations of this problem.

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