Seminars & Colloquia Calendar

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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