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Graduate Student Combinatorics Seminar Sponsored by DIMACS

The Orchard Problem

Quentin Dubroff - Rutgers University

Location:  GSL
Date & time: Wednesday, 20 February 2019 at 12:15PM - 1:15PM

Abstract: The orchard problem asks for the maximum number of collinear triples in a finite set of points in the plane. Very recently, Green and Tao gave an upper bound on this old problem which exactly matches the known lower bound. I will construct the set which achieves this lower bound, and I'll mention some connections with number theory and algebraic geometry. I will also discuss the conjectured generalization of this problem to collinear k-tuples by Erd?s, which is worth 100 dollars.

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