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Graduate Student Combinatorics Seminar Sponsored by DIMACS

Helly's Theorem and generalizations

Quentin Dubroff - Rutgers University

Location:  GSL - Hill 701
Date & time: Wednesday, 13 November 2019 at 12:15PM - 1:15PM

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.

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