Geometry Seminar

---

A point of the interior of convex hulls

Speaker: Imre Bárány, Alfréd Rényi Institute of Mathematics and University College London

Location: Warren Weaver Hall 1314 and on Zoom

Date: Tuesday, March 3, 2026, 6 p.m.

Synopsis:

Abstract. Steinitz's theorem states that if a point a is in the interior of the convex hull of a set \(X\) in R^d, then \(X\) contains a subset \(Y\) of size at most \(2d\) such that the point a lies in the interior of the convex hull of \(Y\) Easy examples show that the bound \(2d\) is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly \(2d\) sets are needed.

Joint work with Yun Qi.

Notes:

In person and on Zoom.  Plz contact Boris Aronov if you are not NYU-affiliated and want to attend in person and/or to be put on the mailing list and get the Zoom information.