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Helly type problems: topology, the cascade conjecture, and graph coloring

Gil Kalai, Hebrew University of Jerusalem, Reichman University, and NYU
Wednesday, November 10, 2021 - 3:30pm to 5:00pm
PDL C-38 and via Zoom Link:
Gil Kalai
Gil Kalai


In the lecture I will start with the notable theorems of Radon and Tverberg and mention the following conjectural extension.

For a set X of points x(1), x(2),...,x(n) in some real vector space V we denote by T(X;r) the set of points in X that belong to the convex hulls of r pairwise disjoint subsets of X. We let t(X;r)=1+dim (T(X;r)).

Radon's theorem asserts that If t(X,1) < |X| then t(X,2) >0.

The first open case of the cascade conjecture asserts that 
If t(X,1)+t(X,2) < |X| then t(X,3) >0.

In the lecture I will discuss connections with topology and with graph coloring.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974