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                * Princeton Discrete Math Seminar *
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Speaker: Daniel McGinnis (Princeton)

Thursday 27th March, 3:00 in Fine Hall 224.

Title: A necessary and sufficient condition for k-transversals

In 1957, Hadwiger proved that if an ordered finite family of pairwise
disjoint convex sets in the plane has the property that for every 3 sets, there
is a line intersecting them in their relative order, then there is a line
intersecting all the sets in the family. This was later generalized to the case
where we wish to intersect a family of convex sets in d dimensions with a
hyperplane by Goodman, Pollack, and Wenger in a series of 3 papers.

We provide an answer to a longstanding open problem of determining a necessary
and sufficient condition for a family of convex sets in d dimensions that
determines the existence of a k-dimensional affine subspace that intersects each
set in the family. This generalizes the previously mentioned results.

This is joint work with Nikola Sadovek.

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