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Colloquium, Spring 2005

Day: Friday June 3rd Time: 3:00pm Place: BH 112 Title: Partitioning of Point Sets in the Plane and Beyond Speaker: Melissa Henry, WWU Abstract: If you have 4 points in the plane, can you partition the four points into two subsets such that the convex hulls of the two subsets have a point in common? What about if you were given d+2 points in R^d? Can you prove that there is a point in common to the convex hulls of the two subsets? In 1922 Radon showed the answer is "Yes!" In the plane, another question that can be asked is what is the fewest number of points needed in order to assure that there exists a partition of the set into three or four or twenty-two subsets such that the intersection of the convex hulls of the subsets have a point in common? Combining these ideas, Tverberg showed in 1966 that m(d+1)-d points are needed need if we want to partition the points into m subsets in R^d whose convex hulls have a common point. In this talk, I will explore the above questions as well as some more generalized questions. Cookies: In BH 300 at 2:30pm.