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Seminar Details

Helly's Theorem and Generalizations

  • Start Date: November 13, 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:

    Helly's theorem states that if any d+1 or fewer elements of a finite family of convex sets in R^d have non-empty intersection then there is a point which is contained in every member of the family. I will present a proof of this theorem and will discuss its foundational role in convex geometry. I will then show how we can extract information about intersection patterns of convex sets by studying simplicial complexes following a paper of Gil Kalai.