Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2017

Speaker:  Florian Frick, Cornell University
Title: The Tverberg admissible-prescribable problem
Time: 2:30 PM, Monday, February 13, 2017
Place:  Malott 206

Abstract: The Tverberg admissible-prescribable problem asks for a topological relaxation of the following convex-geometric question: which dimensions can be prescribed such that in any sufficiently large point set in Euclidean d-space there are convex hulls of those prescribed dimensions that share a common point. The AP conjecture gives a possible characterization of those dimensions. I will construct counterexamples to the AP conjecture, showing a further distinction between results in the affine setting and their continuous generalizations. This is the first instance of such a distinction persisting asymptotically for arbitrarily large point sets.

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