Abstracts
for the Seminar

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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