Seminar Details
The Erdős-Szekeres Conjecture
- Start Date: September 30, 2020
- Event Start Time: 12:15 PM
- Event End Time: 1:15 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Tae Young Lee - University of Texas, Austin
- Event Location: Online Event
- Event Additional Info: <p>Presented via Zoom: <a href="https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Frutgers.zoom.us%2Fj%2F98441409199&data=02%7C01%7C%7C5c0dff3070f84d8a170a08d864acb574%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C637370040219239080&sdata=XomEVUCot4Act%2BOIGWERoDqmFvDdK2VpLP1zhZn2MVs%3D&reserved=0" target="_blank">https://rutgers.zoom.us/j/98441409199</a></p> <p>Password: 715004</p> <p> </p> <p>See: <a href="https://sites.math.rutgers.edu/~qcd2/GCS.html" target="_blank">https://sites.math.rutgers.edu/~qcd2/GCS.html</a></p> <p> </p> <p> </p>
- Presentation Type: Stand Alone Presentation
- 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? Erdős 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.