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Seminar Details

The Orchard Problem

  • Start Date: February 20, 2019
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Quentin Dubroff - Rutgers University
  • Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
  • Presentation Type: Stand Alone Presentation
  • 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 Erdős, which is worth 100 dollars.